# Laser Interactions with Gas Jets: EMP Emission and Nozzle Damage

P. W. Bradford<EMAIL_ADDRESS>Centre Lasers Intenses et
Applications, University of Bordeaux-CNRS-CEA, 33405 Talence, Bordeaux, France
V. Ospina-Bohórquez  Centre Lasers Intenses et Applications, University of
Bordeaux-CNRS-CEA, 33405 Talence, Bordeaux, France  CEA, DAM, DIF, F-91297
Arpajon, France  Université Paris-Saclay, CEA, LMCE, 91680 Bruyères-le-Châtel,
France  M. Ehret  Centro de Láseres Pulsados, Building M5, Parque Científico,
37185 Villamayor, Salamanca, Spain  J.-L. Henares  Centro de Láseres Pulsados,
Building M5, Parque Científico, 37185 Villamayor, Salamanca, Spain  P.
Puyuelo-Valdes  Centro de Láseres Pulsados, Building M5, Parque Científico,
37185 Villamayor, Salamanca, Spain  T. Chodukowski  Institute of Plasma
Physics and Laser Microfusion, 23 Hery St., 00-908 Warsaw, Poland  T.
Pisarczyk  Institute of Plasma Physics and Laser Microfusion, 23 Hery St.,
00-908 Warsaw, Poland  Z. Rusiniak  Institute of Plasma Physics and Laser
Microfusion, 23 Hery St., 00-908 Warsaw, Poland  C. Salgado-López  Centro de
Láseres Pulsados, Building M5, Parque Científico, 37185 Villamayor, Salamanca,
Spain  C. Vlachos  Centre Lasers Intenses et Applications, University of
Bordeaux-CNRS-CEA, 33405 Talence, Bordeaux, France  M.Scisciò  ENEA - Fusion
and Technologies for Nuclear Safety and Security Department, C.R. Frascati,
Frascati, Rome, Italy  M. Salvadori  ENEA - Fusion and Technologies for
Nuclear Safety and Security Department, C.R. Frascati, Frascati, Rome, Italy
Current affiliation: Consiglio Nazionale delle Ricerche, Istituto Nazionale di
Ottica, CNR-INO, Sesto Fiorentino, 50019, Italy  G. Hicks  The John Adams
Institute for Accelerator Science, Blackett Laboratory, Imperial College
London, London, SW7 2BW, UK  J.-R. Marquès  LULI, CNRS, École Polytechnique,
CEA, Sorbonne Université, Institut Polytechnique de Paris, F-91128 Palaiseau
Cedex, France  L. Gremillet  CEA, DAM, DIF, F-91297 Arpajon, France
Université Paris-Saclay, CEA, LMCE, 91680 Bruyères-le-Châtel, France  J. J.
Santos  Centre Lasers Intenses et Applications, University of Bordeaux-CNRS-
CEA, 33405 Talence, Bordeaux, France  F. Consoli  ENEA - Fusion and
Technologies for Nuclear Safety and Security Department, C.R. Frascati,
Frascati, Rome, Italy  V. T. Tikhonchuk  Centre Lasers Intenses et
Applications, University of Bordeaux-CNRS-CEA, 33405 Talence, Bordeaux, France
Extreme Light Infrastructure ERIC, ELI Beamlines Facility, 25241 Dolní
Břežany, Czech Republic

###### Abstract

We present a theoretical model of electromagnetic pulse emission and nozzle
damage from high-power laser interactions with gas jets. As hot electrons are
accelerated beyond the laser channel, they produce a positively-charged plasma
that expands into the ambient gas until it reaches the gas jet nozzle. A
strong plasma potential leads to electrical breakdown that ionises the gas
even faster than the expanding plasma ions. When contact is made between the
plasma and the conducting nozzle surface, a discharge current propagates to
ground and an electromagnetic pulse is radiated via an antenna emission
mechanism. Damage to gas jet nozzles is caused by heating from plasma ions
rather than Ohmic heating via a discharge current. Our model agrees with
experimental data from experiments on proton acceleration in near-critical
plasmas at the Vulcan and VEGA-3 lasers.

August 28, 2024

##  I Introduction

High-power laser pulses focused into dense gases are used for the acceleration
of charged particles and the generation of hard x-ray radiation, but these
interactions also produce undesirable secondary effects, such as nozzle damage
and the emission of electromagnetic pulses (EMPs). Laser-driven EMPs are
produced in the radio-frequency domain and couple to motors, computers and
other electronic equipment. On the VEGA-3 laser system [1] at CLPU, EMPs have
been responsible for valve malfunctions and gas leaks from jet nozzles; they
are also known to enter diagnostics and oscilloscopes - ruining measurements
of charged particle emission.

Megahertz- and gigahertz-frequency EMPs are generated in a variety of high-
power laser experiments when hot electrons are expelled from the target and
oscillating currents are excited in the target mount and surrounding chamber
[2]. Previous research [3, 4, 5, 6, 7] has focused on laser interactions with
solid targets, where the EMP amplitude is known to be the highest. The few
measurements available for high-density gas jet targets [8, 9], however,
suggest that EMP emission is significant. If the EMP amplitude from gas jets
scales with laser energy and intensity as for solid targets, these EMP fields
will increase with a new generation of ultra-intense, high-repetition-rate
laser systems [10].

A second important concern of the laser-gas interaction is damage to the gas
jet nozzle. Many of the most exciting applications of laser-gas research rely
on high shot rates and a reproducible gas density profile to generate bright,
high-fluence sources of energetic ions [11, 12, 13, 14, 15, 16], electrons[17,
18] or x-rays [19, 20]. Repeated melting of the gas nozzle therefore
represents a serious and expensive hindrance to this research. On energetic
systems like the Vulcan Petawatt laser [21, 22] at the Rutherford Appleton
Laboratory, a single shot on a dense gas target is sufficient to destroy the
gas nozzle completely (see Fig. 1). For systems operating at lower energy,
lower gas density and shorter pulse duration, nozzle damage is more
progressive but still leads to significant smoothing of the gas density
profile [23, 24], degradation of the laser interaction and reduced data
reproducibility. Understanding the nozzle damage mechanism is therefore
important for future laser-gas applications.

Figure 1: Gas jet nozzle used during an experiment at Vulcan Target Area
Petawatt (a) before and (b) after a full-power laser shot. Melting can lead to
occlusion of the nozzle aperture or even total rupture of the material. Images
reproduced from Hicks et al. [25] with permission.

To date, no theoretical framework has been proposed for the emission of EMP
from gas jets and this makes it difficult to estimate the severity of its
impact on new laser systems. In Sec. II and Sec. III.1-III.3, we present a
model of laser-plasma expansion in a gas, where ionisation is mainly caused by
ions streaming from the laser focus (anode) to the nozzle (cathode). In Sec.
III.4, however, we show that electrical breakdown induced by a strong plasma-
nozzle potential can fully ionise the gas on shorter timescales of 10-20 ps.
EMP is then emitted similarly to solid target interactions, where a discharge
current propagates to ground (the chamber) along a cm-scale antenna (the
nozzle or target support), emitting radiation at gigahertz frequencies.
According to our model, the EMP amplitude for Vulcan Petawatt and VEGA-style
interactions can reach $\sim 100$ $\mu$T or $\sim 100$ kV/m at a distance
$\sim 1$ m from the target. The theoretical model is supported in Sec. VI by
the results from two experiments on the VEGA-3 laser, which show reasonable
agreement with the discharge time, magnetic field spatial profile and
accumulated target charge.

Using the plasma expansion model in Sec. V, we consider how the nozzle may be
damaged. Two mechanisms are considered: (i) a kA-level discharge current and
(ii) ion collisional heating. We show that damage to gas jet nozzles is more
likely caused by the impact of plasma ions than Ohmic heating of the nozzle
surface. Finally, in Sec. VII, we present ideas for how the EMP emission model
can be reliably benchmarked with simulations and dedicated experiments. The
practical impact of this work is broad: allowing scientists to reduce damage
to expensive gas jet nozzles and minimize the electrical disruption of
equipment. It likewise represents a rich seam of more fundamental research,
connecting the physics of laser-target charging, ionisation, ion acceleration,
high-voltage breakdown and antenna emission.

##  II Expansion of a Laser-Plasma in a Gas Jet

We consider an expanding plasma created as a laser pulse propagates through a
high-density gas. The laser pulse ionises the gas and creates a plasma
channel. The plasma electrons are heated by the laser radiation to
relativistic energies, and some of them escape the channel and leave it
positively charged. This charged plasma cylinder then expands, ionising the
gas until it makes contact with the conducting tip of the gas nozzle. Once
contact has been made, the plasma is connected directly to the ground via the
nozzle. A discharge is triggered and EMP radiation is emitted. Nozzle damage
is determined variously by the amount of energy stored in the plasma, the
strength of the discharge and the nozzle material.

Starting from some characteristic gas and laser parameters, we first explore
the physics of plasma expansion, electrical discharge and EMP emission. By way
of example, we consider the Vulcan-Petawatt laser, with pulse energy
$E_{L}=200$ J, duration $\tau_{L}=600$ fs and wavelength
$\lambda_{L}=1.053\,\mu$m [25]. The laser beam is focused using $f_{\\#}=3$
optics to a spot with full width at half maximum (FWHM) $w_{L}=3.9\,\mu$m.
Only 40% of the total laser energy is contained within the FWHM, for a maximum
on-target intensity of $I_{L}\simeq 2.9\times 10^{20}$ W cm-2. The spatial
extent of the laser channel in the gas depends on the wavelength of the laser
and the gas density. For typical gas pressures $p_{\rm gas}$ ranging from 0.03
to 30 bar, the atomic/molecular densities in the laser focal region are in the
range $n_{\rm gas}\sim 10^{18}-10^{21}$ cm-3. The maximum electron density in
a fully ionised plasma is smaller than the critical density, so the laser can
propagate through the gas.

The Rayleigh length of a diffraction-limited Gaussian beam in our example is
$Z_{R}=\pi w_{L}^{2}/\lambda_{L}\simeq 44\,\mu$m. Since the gas jet width is
usually larger than $Z_{R}$, the laser produces a channel a few times longer
than $Z_{R}$ that can be viewed as a $l_{p}\simeq 0.5$ mm-long plasma cylinder
created at a typical height of $h\simeq 0.5$ mm above the nozzle. We take the
initial radius of the plasma channel to be a factor of a few times larger than
the laser focal radius, $r_{p}=20\,\mu$m, to reflect the average size of the
channel as the laser deposits energy over the full length of its path through
the gas. The laser absorption in the gas jet is $\eta_{L}\sim 90$%, with 40%
transferred to hot electrons. This is consistent both with Particle-in-Cell
(PIC) simulations[25, 26] and experimental interferograms [27], which show
that a high-power laser pulse deposits a large fraction of its energy in the
gas jet and leaves behind it a plasma channel several tens of microns wide.

Parameter | Vulcan-TAP | VEGA-3
---|---|---
Gas | H2 | He
$\lambda_{L}$ [$\mu$m] | 1.05 | 0.8
$E_{L}$ [J] | 80 | 8
$\tau_{L}$ [fs] | 600 | 75
$f_{\\#}$ | 3 | 10
$w_{L}$ [$\mu$m] | 3.9 | 9.8
$I_{L}$ [W cm-2] | $2.9\times 10^{20}$ | $3.6\times 10^{19}$
$a_{0}$ | 15 | 4.1
$\eta_{L}$ | 0.9 | 0.9
$\eta_{\rm las\rightarrow e}$ | 0.4 | 0.1
$p_{\rm gas}$ [bar] | 15 | 4.5
$h$ [$\mu$m] | 500 | 500
$r_{p}$ [$\mu$m] | 20 | 20
$V_{p}$ [cm3] | $6\times 10^{-7}$ | $6\times 10^{-7}$
$n_{e}$ [cm-3] | $8.1\times 10^{20}$ | $4.8\times 10^{20}$
$T_{e}$ [keV] | 280 | 77
$T_{h}$ [MeV] | 5.0 | 1.1
$\Phi_{p}$ [MV] | 25 | 4.4
$Q$ [nC] | 230 | 42
Table 1: Representative experimental parameters - as described in the text and
Refs. [25, 23] \- and estimates of plasma characteristics according to the
model presented in Sec. II. The plasma radius $r_{p}$ and the laser energy
fraction converted to hot electrons $\eta_{\rm las\rightarrow e}$ are
estimated from dedicated PIC simulations. Values are given to 2 significant
figures.

The parameters of the experiments considered in this paper are given in Tab. 1
along with predictions from our model. Depending on the nozzle design and
envisioned application, the laser pulse can be sent parallel to the surface of
the nozzle tip at a height varying from a few tenths of a millimetre to a few
millimetres. The width of the laser channel also depends on the laser focusing
optics, laser power, and gas density profile along the laser axis. Figure 2
gives a schematic overview of the situation.

Figure 2: Schematic of the nozzle, gas and the cylindrical plasma channel
formed by the laser. Here, $r_{p}$ is the radius of the plasma cylinder, $h$
is the separation between the channel and the nozzle, and $\Phi_{p}$ is the
electric potential. The laser is directed into the page, along the axis of the
plasma. Red crosses indicate a region of positive charge inside the laser-
generated channel. Three curved arrows show the geometry of the electric
field, E.

###  II.1 Electric Charging of the Plasma

Following the available observations and numerical simulations [28, 29, 30,
31], we assume that the plasma in the laser channel is fully ionised. The
absorbed laser energy $\eta_{L}E_{L}$ is transferred to electrons with an
energy distribution approximated by a two-temperature distribution:

$f_{e}(\gamma)=n_{e}f_{\rm MJ}(\gamma,\Theta_{e})+n_{h}f_{\rm
MJ}(\gamma,\Theta_{h}),$ (1)

where $f_{\rm MJ}(\gamma,\Theta)$ is the Maxwell-Jüttner function

$f_{e}(\gamma,\Theta)=(\gamma/\Theta)\,K_{2}(1/\Theta)\sqrt{\gamma^{2}-1}\exp(-\gamma/\Theta)$

depending on the dimensionless temperature $\Theta=T/m_{e}c^{2}$, the second
order Bessel function $K$ and the electron relativistic factor
$\gamma=1+\varepsilon/m_{e}c^{2}$. A fraction $\eta_{\rm las\to e}$ is
transferred to a population of hot electrons with density $n_{h}$ and
temperature $T_{h}$, while the remaining energy goes to electrons in the
plasma bulk, with density $n_{e}$ and temperature $T_{e}$.

The bulk electron density is defined by the gas density ($n_{e}=n_{\rm at}$
for hydrogen) and the bulk temperature is defined by the plasma volume and
deposited energy via:

$C_{e}(T_{e})n_{e}T_{e}=(1-\eta_{\rm las\to e})\eta_{L}E_{L}/V_{p},$ (2)

where $C_{e}(T_{e})=3-[1-K_{1}(1/\Theta_{e})/K_{2}(1/\Theta_{e})]/\Theta_{e}$
is the heat capacitance of a relativistic electron gas. For the parameters of
the Vulcan experiment given in Tab. 1, a plasma channel of radius
$r_{p}=20\,\mu$m and length $l_{p}=0.5$ mm has volume $V_{p}=\pi
r_{p}^{2}l_{p}\simeq 6\times 10^{-7}$ cm3. A hydrogen gas pressure of 15 bar
corresponds to an atomic gas density $n_{\rm at}\simeq 8.1\times 10^{20}$ cm-3
at a distance $h\simeq 0.5$ mm above the nozzle, so we have $N_{e}\simeq
5.1\times 10^{14}$ electrons. Equation (2) yields an effective electron
temperature $T_{e}=250$ keV for the total bulk energy of 43 J.

To estimate the hot electron density, we prescribe a hot electron temperature
of $T_{h}=5.0$ MeV following the ponderomotive scaling[32]. The hot electron
density can then be defined knowing the fraction of energy transferred to hot
electrons $\eta_{\rm las\to e}$:

$C_{e}(T_{h})n_{h}T_{h}=\eta_{\rm las\to e}\eta_{L}E_{L}/V_{p}.$

On Vulcan, the hot electron fraction is $n_{h}/n_{e}\simeq 2.5$% and their
total energy is 29 J.

The electric potential of the plasma channel is determined by how many hot
electrons can overcome the plasma potential barrier. The electric potential
$\Phi_{p}$ at the surface of the plasma cylinder with respect to the grounded
nozzle can be estimated as

$\Phi_{p}=Q/C,$ (3)

where $Q$ is the charge of the plasma and $C=2\pi
l_{p}\epsilon_{0}/\ln(h/r_{p})$ is the capacitance. Only electrons with
energies $\varepsilon_{e}>e\Phi_{p}$ can escape plasma to the ground.
Assuming, as mentioned above, that hot electrons have an exponential
distribution in energy with a temperature $T_{h}$, the fraction of escaped hot
electrons is [33]:

$\frac{\delta n_{h}}{n_{h}}=\int_{1+\psi}^{\infty}d\gamma\,f_{\rm
MJ}(\gamma,\Theta_{h}),$ (4)

where $\psi=e\Phi_{p}/m_{e}c^{2}$ is the dimensionless potential. The plasma
charge is then $Q=e\delta n_{h}V_{p}$ and, substituting this expression into
Eq. (3), we have the following equation for the dimensionless potential
$\psi$:

$\psi=\frac{r_{p}^{2}\omega_{ph}^{2}}{2c^{2}}\,\frac{\delta
n_{h}}{n_{h}}\,\ln\frac{h}{r_{p}},$ (5)

where $\omega_{ph}=(e^{2}n_{h}/m_{e}\epsilon_{0})^{1/2}$ is the hot electron
plasma frequency. Solution of this equation for $h/r_{p}=250$ and
$r_{p}\omega_{ph}/c=18$ gives $\Phi_{p}=24.8$ MV. Knowing the plasma potential
and the plasma capacitance $C\simeq 0.0086$ pF, we find the charge ejected
from the plasma column, $Q=C\Phi_{p}\simeq 234$ nC. This corresponds to a
fraction of escaped electrons $\delta n_{h}/n_{e}\approx 2.8\times 10^{-3}$
and is consistent with the experiment [34]. Since the time required for a hot
electron to cross the channel is relatively short ($\sim 2r_{p}/c\sim 0.13$
ps), the time of plasma charging is determined by the time of flight of the
laser pulse through the gas, $\sim 3$ ps.

The total energy of escaped electrons

$\mathcal{E}_{\rm
esc}=V_{p}n_{h}m_{e}c^{2}\int_{1+\psi}^{\infty}d\gamma\,(\gamma-1)f_{\rm
MJ}(\gamma,\Theta_{h})$

is split between the electrostatic energy of the charged plasma
$\mathcal{E}_{\rm es}=Q^{2}/2C\simeq 3.2$ J and the kinetic energy of the
escaped electrons $\simeq 4.2$ J.

###  II.2 Ion Acceleration in Expanding Plasma

Following a short phase of gas ionisation, electron heating and plasma
charging, the plasma expands and cools down. The time required for the plasma
to expand from the laser-generated channel to the nozzle defines the plasma
discharge time. In Sec. IV, we show that the discharge time determines the
energy and amplitude of the radiated EMP. Plasma x-ray emission and laser-
accelerated fast electrons and ions, as shown in Sec. III, partially ionise
the gas and provide seed electrons for a discharge via electrical breakdown.

After the end of the laser pulse, there is no more energy supply and the
plasma expands adiabatically under the electron thermal pressure. For the
plasma parameters given above, the pressure $p_{e}=n_{e}T_{e}\simeq 330$ Mbar
is much higher than the ambient gas pressure, so the plasma expands freely
with electrons transferring their energy to ions. The plasma charge is
conserved during the expansion phase and the potential decreases
logarithmically as the plasma radius increases (see Eq. (3)). The plasma
expansion can be described in some special cases by a self-similar rarefaction
wave model [35, 36]. More detailed analysis is performed for a spherical
plasma expansion in Ref. [37]. The ion energy distribution depends on the
density profile and on the ratio of the plasma radius to the Debye length. For
our crude estimates, it is sufficient to estimate the average ion kinetic
energy by dividing the deposited laser energy by the number of ions in the
plasma. For a hydrogen plasma, it is 1.5 times the bulk electron temperature
$\varepsilon_{i}\simeq 0.4$ MeV. This corresponds to an ion velocity of
$v_{i}\simeq 9\,\mu$m/ps, and an ion expansion time to the nozzle $t_{\rm
exp}\simeq 60$ ps. The total energy carried by these ions is of order the bulk
electron energy - that is, about 40 J for the Vulcan experiment.

In addition to ions accelerated by bulk electron pressure in the expanding
plasma, some ions are accelerated to energies of a few MeV in the
electrostatic field created by the escaped electrons. Hicks et al. [25] report
on the number of such fast protons accelerated in the radial direction as 30
nC/sr. Assuming an emission solid angle of $1-2$ sr, the total charge of
ejected protons is about 60 nC and their overall energy about 0.2 J. These
values are consistent with 230 nC charge of ejected electrons and a
corresponding energy of $\sim 4$ J, as estimated above.

##  III Gas Ionisation by Laser-Plasma Products

The level of EMP emission depends on the intensity of the discharge current
and, consequently, the resistance of the plasma that connects the laser
channel to the nozzle. There are four processes of gas ionisation: (i)
photoionisation from UV and x-rays produced by the bremsstrahlung of hot
electrons in the plasma column, (ii) collisional and field ionisation from
fast electrons accelerated in the laser channel, (iii) collisional ionisation
from fast ions emanating from the laser channel and (iv) ionisation by
electron avalanche caused by a high plasma-nozzle electric potential.

###  III.1 X-ray Photoionisation of the Gas

The bremsstrahlung emission of electrons in the laser-created plasma covers a
broad range of photon energies up to the electron kinetic energy. Assuming the
electron energy distribution is characterized by an effective temperature
$T_{e}$, the power of bremsstrahlung emission from a hydrogen plasma can be
written as [38]:

$P_{\text{Brem}}=1.69\times 10^{-32}n_{e}^{2}T_{e}^{1/2}\,{\rm
W\leavevmode\nobreak\ cm}^{-3},$

where the electron density is in cm-3 and the electron temperature is in eV.
For an electron density of $n_{e}=8\times 10^{20}$ cm-3 in fully ionised
plasma and a temperature $T_{e}\simeq 250$ keV, we have
$P_{\text{Brem}}=6\times 10^{12}$ W cm-3. Accounting for the plasma volume of
$V_{p}\sim 6\times 10^{-7}$ cm3 and lifetime $t_{\rm exp}\sim 60$ ps, the
total radiated energy is about $\mathcal{E}_{\rm Brem}=P_{\rm Brem}V_{p}t_{\rm
exp}\simeq 0.2$ mJ. The spectrum of emission is flat for photons with energy
$\varepsilon_{x}\lesssim T_{e}$ and decreases exponentially with a temperature
$T_{\rm rad}\simeq T_{e}$ for higher energies.

The mean free path of photons with energies above 3 keV in hydrogen is
approximately constant at $\lambda_{x}\rho_{\rm gas}\sim 3$ g cm-2 [39]. For a
gas jet density of $\rho_{\rm gas}\sim 1.3$ mg cm-3, the absorption length is
20 m and the probability of gas ionisation over a millimetre distance is
negligible. The mean free path of lower energy photons strongly decreases as
the energy decreases [39], however. It can be approximated by
$\lambda_{x}\rho_{\rm gas}\sim 10^{-10}\varepsilon_{x}^{3}$ g cm-2 for
hydrogen, where $\varepsilon_{x}$ is the photon energy in eV. The mean free
path of photons with the energy of $15-20$ eV - comparable to the hydrogen
ionisation potential $U_{\rm ion}=13.6$ eV - is therefore just a few microns.

The photons with energy about $\varepsilon_{h}\sim 100-200$ eV produce the
most efficient photoionisation because their mean free path is comparable to
the plasma-nozzle distance. The fraction of bremsstrahlung energy carried by
these photons is $\varepsilon_{h}/T_{e}\sim 10^{-3}$ \- that is, about
$0.2\,\mu$J. Knowing the energy required to ionise a hydrogen atom and the
volume of gas between the plasma and the nozzle, $V_{\rm gas}\sim 4\times
10^{-4}$ cm3, the gas ionisation level can be estimated as $\mathcal{E}_{\rm
Brem}\varepsilon_{h}/T_{e}U_{\rm ion}V_{\rm gas}\sim 1.7\times 10^{14}$ cm-3.
This corresponds to an ionised fraction of approximately $3\times 10^{-7}$.
The photoionisation time of $\sim 60$ ps is defined by the time of
bremsstrahlung emission, which is the lifetime of the hot plasma channel.

###  III.2 Ionisation by Hot Electrons

Hot electrons also contribute to the ionisation process. These electrons are
those escaping the plasma potential barrier and their characteristics are
estimated in Sec. II. The stopping power of electrons in hydrogen gas for this
range of energies of a few MeV is $\sim 4$ MeV cm2/g [40], so a hot electron
loses $\sim 260$ eV over the distance $h\simeq 0.5$ mm. The energy of
secondary electrons is comparable to the ionisation potential of the gas [41],
which means that one primary electron creates $\sim 20$ secondary electrons in
the gas volume. Using the number of escaped electrons estimated in Sec. II.1,
$N_{\rm esc}\simeq 1.4\times 10^{12}$, the density of secondary electrons
produced by collisional ionisation is $\sim 7.5\times 10^{16}$ cm-3. This
corresponds to an ionised fraction of $\sim 10^{-4}$, which is produced in a
short time of hot electron emission of a few ps.

Alternatively, hot electrons can produce field ionisation of the gas if the
electron beam density is sufficiently high. For a beam of 3 MeV electrons
passing through a neutral gas, field ionisation dominates over collisional
ionisation for beam densities exceeding $\sim 10^{17}$ cm${}^{-3}\,$ [42].
Considering $10^{12}$ hot electrons contained within the initial plasma
volume, the maximum beam density is $\sim 2.5\times 10^{17}$ cm-3. So field
ionisation has approximately the same impact as collisional ionisation.

###  III.3 Ionisation by Plasma Ions

The stopping power of a representative 0.4 MeV proton in hydrogen is 1200 MeV
cm2/g [43]. The energy needed for the creation of one secondary electron by a
fast ion is of order the ionisation potential, $U_{\rm ion}$, and it varies
weakly with the ion energy[44, 45]. A 0.4 MeV proton passing through hydrogen
gas therefore creates $\sim 6000$ secondary electrons over the 0.5 mm distance
between the plasma and the nozzle, losing about 0.1 MeV of its kinetic energy.
In a gas volume of $\sim 4\times 10^{-4}$ cm-3, this corresponds to complete
ionisation of the ambient gas. This is, however, a relatively long process
that takes $\sim 60$ ps.

The contribution of fast ions to gas ionisation is smaller by more than three
orders of magnitude, but their velocity is about three times higher. An
ionisation level of $\sim 3\times 10^{-3}$ is therefore produced prior to
plasma expansion, during the time of flight of the fast ions, which is about
20 ps.

In conclusion, photoionisation of the gas jet is low and can be neglected.
Instead, ionisation by charged particles is produced in three steps: first, at
the level of $10^{-4}$ by fast electrons in a few ps, then at the level of
$10^{-3}$ by fast ions within 20 ps, then finally by the expanding plasma on a
timescale of 60 ps. Free electrons produced during the first two steps provide
the seed for a discharge by electrical breakdown, as discussed in the next
section.

###  III.4 Gas Ionisation by Electrical Breakdown

When hot electrons are ejected from the laser plasma, it becomes positively
charged with respect to the nozzle. The electric field between the plasma and
nozzle may then break down the gas and propagate a discharge. The discharge
regime is determined by the product of the gas pressure and electrode
separation $p_{\rm gas}h$. Under Vulcan-like conditions, with $p_{\rm
gas}h\gtrsim 1$ bar cm, avalanche ionisation will occur if the potential is
above the breakdown value of $20-30$ kV. This is much smaller than the plasma
potential of $\sim 25$ MV estimated in Sec. II.

In the avalanche process, the electron density increases exponentially in time
from the seed level $n_{e0}/n_{\rm at}\sim 10^{-4}-10^{-3}$ created by fast
electrons or ions, $n_{e}(t)=n_{e0}\,\exp(t/\tau_{\rm ion})$, where $\tau_{\rm
ion}$ is the characteristic ionisation time. A high electrostatic potential
means the ionisation time is very short, $\tau_{\rm ion}\sim 1$ ps. However,
the plasma potential decreases with time for two reasons: first, it decreases
logarithmically with time because of plasma expansion according to Eq. (3) and
second, because the energy deposited during the ionisation process is
extracted from the electrostatic energy. The decrease in electrostatic energy
is related to the ionisation loss, $\simeq U_{\rm ion}n_{e}V_{\rm gas}$, and
the discharge stops when $\mathcal{E}_{es}\sim U_{\rm ion}V_{\rm gas}n_{e}$.
This relation defines the maximum ionisation that can be achieved by avalanche
breakdown, $n_{e,\max}\sim 4\times 10^{21}$ cm-3, which is larger than the
atomic gas density.

In conclusion, avalanche breakdown produces a higher level of ionisation than
fast electrons or fast ions on a $10-20$ ps timescale, and it can fully ionise
the gas under the conditions of the Vulcan experiment before the expanding
plasma reaches the nozzle.

###  III.5 Plasma Resistance

The degree of gas ionisation determines the plasma resistance and the
discharge current that can be supported. We estimate the plasma resistance as
$R=\eta h/A$, where $\eta$ is the plasma resistivity and $A\approx
2r_{p}l_{p}$ is the cross-sectional area of the ionised gas between the nozzle
and the laser channel. The plasma resistivity in a fully ionised plasma is
dominated by electron-ion collisions and can be estimated from the Drude
formula:

$\eta=m_{e}\nu_{ei}/e^{2}n_{e},$ (6)

where $\nu_{ei}$ is the electron-ion collision frequency. Assuming the
electron temperature to be of the order of the ionisation potential, we find
$\nu_{ei}\sim 10^{14}$ s-1 and the plasma resistivity is $\eta\simeq 5\times
10^{-6}\,\Omega$ m. This corresponds to a very small resistance of order
$0.1\,\Omega$, so as soon as the gas is fully ionised, the plasma potential is
applied to the nozzle and a discharge current is produced.

##  IV EMP emission

Here, we estimate the characteristics of EMP emission. The theoretical picture
is as follows: the plasma supplies a current limited by the nozzle resistance
and the available charge and radiation is emitted from an antenna made out of
the conducting parts of the nozzle. Considering the nozzle as a quarter-
wavelength dipole, the emission frequency depends on the nozzle length $h_{d}$
as $\nu_{\rm emp}=c/4h_{d}$. For $h_{d}=3$ cm, the emission frequency is 2.5
GHz.

The EMP energy is limited by the available electrostatic energy in the plasma,
which is of order a few joules. Modelling the plasma-nozzle system as a
dipole, the total emitted energy, according to the textbook by Jackson [3],
depends on the charge $Q$ and the emission frequency:

$\mathcal{E}_{EMP}\approx 0.1Z_{0}Q^{2}\nu_{\rm emp}$ (7)

where $Z_{0}=377$ $\Omega$ is the vacuum impedance. For 230 nC accumulated
charge and an emission frequency of 2.5 GHz, the relation yields $\sim 5$ mJ
of EMP energy and an average current at the antenna frequency[46] of
$J_{\text{emp}}=Q\nu_{\rm emp}\sim 580$ A. EMP emission is delayed with
respect to the laser: first, because it takes time to ionise the gas and
second, because the current needs time to propagate along the antenna.

Knowing the amplitude of the discharge current, we can also estimate the
amplitude of the emitted magnetic field at a distance $r$ as
$B\simeq\mu_{0}J_{\text{emp}}/2\pi r$. For a nozzle of height $h_{d}=3$ cm,
the peak magnetic field amplitude is $\sim 120$ $\mu$T at a distance of $r=1$
m. The gas discharge is thus expected to produce an electromagnetic pulse with
electric field of amplitude $E=cB\approx 36$ kV/m (in the plane wave
approximation). This value is higher than the electromagnetic susceptibility
threshold for electronics [47].

##  V Nozzle Damage Mechanism

We identify two mechanisms that could lead to nozzle damage in high-power
laser experiments with gas jets: Ohmic heating from a discharge current or
bombardment by plasma ions. To evaluate which process is more likely to induce
melting, we calculate the energy required to melt a given mass of nozzle
material.

We consider copper as a representative nozzle material, with a heat capacity
$C_{V}=0.39$ J/gK, a melt temperature of 1360 K and a latent heat of melting
0.86 kJ/g. To heat 1 g of Cu to the melting temperature - and to melt it - one
needs a total energy of 1.3 kJ. Similar estimates apply to aluminium and iron.
The total available electrostatic energy in the plasma of 3 J can melt a
maximum of 2 mg Cu. By contrast, the kinetic energy of the expanding plasma is
more than 10 times larger. The plasma can therefore cause more damage to the
nozzle.

###  V.1 Energy Released through Ohmic Heating

The energy released by Ohmic heating is $J^{2}Rt_{p}$, where $J=Q/t_{p}$ is
the discharge current. The resistance $R$ is calculated from the metal
resistivity $\eta_{d}$ and the current-carrying surface $A_{d}$ and nozzle
length $h_{d}$. Since the discharge is short, the current is confined within a
skin depth, $\delta=\sqrt{\eta_{d}/\nu_{\rm emp}\mu_{0}}$. For Cu resistivity
$\eta_{d}=1.7\times 10^{-7}\,\Omega$ m and the frequency $\nu_{\rm emp}\approx
2.5$ GHz, the skin depth is $\delta\sim 10\leavevmode\nobreak\ \mu$m. Assuming
the current flows along $h_{d}=3$ cm nozzle with a radius of $r_{d}=5$ mm, the
current-carrying cross-sectional area is $A_{d}\sim 3\times 10^{-3}$ cm2 and
the resistance is $R=\eta_{d}h_{d}/A_{d}\approx 0.01\,\Omega$. The energy
released by Ohmic heating with a 4 kA current over $t_{p}\sim 60$ ps is
therefore $\approx 10\,\mu$J.

Will the conducting layer melt if it is supplied with $10\,\mu$J of heat
energy? The heat conductance length over the heating time is smaller than the
skin depth, so the heating is confined within the skin depth. The volume of
heated material is therefore $h_{d}A_{d}\sim 10^{-2}$ cm3, which gives a
heated mass of $\sim 80$ mg. The available electrostatic energy is not
sufficient to heat such a large mass, so it is unlikely that the melting of
gas nozzles is caused by Ohmic heating from a discharge current.

###  V.2 Heating caused by Plasma Deposition

Plasma ions are the primary source of nozzle heating. Assuming that $N_{i}$
ions in the plasma are expanding isotropically, the angular ion flux is
$N_{i}/4\pi$. The solid angle subtended by the nozzle is given by
$2\pi(1-\cos\alpha)$, where $\tan\alpha=r_{d}/h$. For $h=0.5$ mm and $r_{d}=5$
mm, the solid angle is approximately $2\pi$ and the number of ions incident on
the nozzle is around half the ion population.

The stopping power of 0.4 MeV protons in Cu is 166 MeV cm${}^{2}/$g [43] and
the rate of energy deposition is $\sim 1500$ MeV/cm. The ions therefore
deposit all their energy over a distance $\lesssim 10\leavevmode\nobreak\
\mu$m. The maximum heated volume is $8\times 10^{-6}$ cm3 and the mass of
heated material is $\sim 0.02$ mg.

Based on the estimates of plasma density and volume from Sec. II.1, there are
$N_{i}\sim 5\times 10^{14}$ ions at energy $\sim 0.4$ MeV for a combined
energy of 40 J. Half of these ions strike the nozzle and deposit an energy of
250 kJ/g. This is more than 100 times higher than the energy required to melt
Cu, so plasma heating melts the nozzle easily.

The same conclusion applies to a ceramic nozzle, even with the greater heat
resistance. Consider SiC with a melting temperature of 3100 K, 370 J/g latent
heat of melting and a specific heat capacity of $0.67-1.4$ J/gK for
temperatures between $300-4000$ K [48]. Using these values, we find that $\sim
4$ kJ/g is required to melt SiC. According to the NIST proton stopping
catalogue, the stopping power of a 0.5 MeV proton in SiO2 is 290 MeV cm2/g
[43]. For a density of 3.2 g cm-3, the rate of energy deposition is 1000
MeV/cm, and the deposition depth is $\sim 5\,\mu$m, for a heated volume of
approximately $2\times 10^{-5}$ cm3 and a heated mass of $0.06-0.1$ mg. This
is consistent with SRIM Monte Carlo simulations [49] of 0.4 MeV protons
incident on SiC, which give a $4\,\mu$m range. 20 J of incident ion energy
deposited in a few microns corresponds to heating of $\sim 2$ MJ/g - more than
sufficient to melt the ceramic.

This conclusion is supported by a gas jet experiment on the VEGA-3 laser [50].
The laser was focused to an intensity of $2.2\times 10^{19}$ W cm-2 in a He
(97%) and H2 (3%) gas mix with peak atomic densities of order $\sim 10^{21}$
cm-3 (see Sec. VI.2 for more details of the experiment). Tungsten nozzles
suffered progressive damage over tens of shots when the laser was focused at a
distance $\sim 900\,\mu$m, whereas a UV fused silica nozzle was destroyed when
the laser was focused at a distance of $400\,\mu$m from the nozzle surface.

We can apply this model of nozzle damage to a Vulcan-style experiment. The
amount of energy deposited by the ions is sensitive to the number of ions and
their average energy. Taking a vertical gas density profile from measurements
by Hicks et al. [25], we estimate the number of ions generated in the laser
channel when the laser is focused at different heights above the gas jet. We
assume a value of $N_{i}$ at a fixed height of $160\,\mu$m, where the density
is maximal, and scale it by the normalised vertical density profile as the
laser focus is shifted to different heights above the nozzle. Following the
method outlined earlier, we then calculate the ion flux on the nozzle surface
and the amount of energy deposited when the laser is focused at different
distances from the nozzle. Hicks et al. observed that metallic nozzles were
instantly destroyed at a nozzle-focus distance of $400\,\mu$m and virtually
undamaged when they were separated by 2 mm. Since the melt threshold for Cu is
1.4 kJ/g, this suggests that the ion energy deposition must reach 2 kJ/g when
the laser is focused somewhere between these two distances. We therefore have
bounds on the total number of 0.4 MeV plasma ions produced by the laser at a
height of $160\,\mu$m, which satisfies $4\times 10^{12}<N_{i}<2\times
10^{14}$. The product of the initial plasma volume and peak gas density gives
a maximum electron number of $\sim 5\times 10^{14}$, which may be considered
an upper limit on the number of accelerated ions.

Figure 3: Ion energy deposited per mass of nozzle material (Cu or Fe) as a
function of laser-nozzle separation for the number of ions $N_{i}=4\times
10^{12}$ (a) and $2\times 10^{14}$ (b) normalised to the plasma height of
$160\,\mu$m. The red dot represents the theoretical melt threshold for a Cu
nozzle. Red and green vertical dashed lines represent observed distances where
a steel nozzle was destroyed and survived, respectively. The ion energy is 0.5
MeV.

The situation is illustrated graphically in Fig. 3. The left panel shows the
ion energy deposited in the nozzle as a function of distance, assuming
$4\times 10^{12}$ plasma ions at 0.5 MeV when the laser is focused at a height
of $160\,\mu$m. The right panel shows the energy deposition for $2\times
10^{14}$ plasma ions at a height of $160\,\mu$m above the nozzle. The amount
of nozzle heating increases as the laser approaches the peak gas density at
$\sim 160\,\mu$m and then drops steeply as the laser is focused further away
from the nozzle. This is caused partially by the reduced solid angle subtended
by the nozzle and also the changing gas density profile. Accounting for ion
collisions in the gas before they reach the nozzle means that less overall
energy is deposited in the nozzle, but the energy per unit mass of heated
material increases due to a higher ion stopping power at lower energies.

The estimates presented in this section suggest that nozzle damage is caused
primarily by ion energy deposition rather than a resistive current, so nozzle
material has little impact on nozzle survival. On the other hand, just as for
EMP emitted from solid targets, the discharge current and EMP amplitude and
spectrum change when one moves from conducting to dielectric nozzles.

##  VI Experimental Results

###  VI.1 Ion Acceleration Experiment on VEGA-3

An experiment was conducted on the VEGA-3 laser system with the aim of using
PW laser pulses to trigger laser channelling in inert gases (He, N2, He-N2)
and thereby learn more about ion acceleration mechanisms [23, 51, 24].

A two-lens imaging system was used to monitor the focal spot diameter during
the experiment, which was fixed at $\sim 12\leavevmode\nobreak\ \mu$m FWHM. A
laser pulse duration of $\tau_{L}=72\pm\leavevmode\nobreak\ 24$ fs was
measured using an autocorrelator. The laser energy varied in the $18.4\pm
2.3\,\rm J$ range (uncertainties correspond to the standard deviation over
$\sim 100$ shots), though only $\sim$47% of the pulse energy is contained
within the focal spot[23]. Two types of shock nozzle were used: Sourcelab
J2021 nozzles (peak atomic density $n_{\rm at,max}\approx 5\times 10^{20}$
cm-3 at a height of $\sim 500\leavevmode\nobreak\ \mu$m above the nozzle) and
S900 nozzles [52] (peak atomic density $n_{\rm at,max}\approx 10^{20}$ cm-3 up
to $\sim 900$ $\mu$m above the nozzle). The S900 nozzles were designed to
produce a convergent shock further from the nozzle surface than the J2021
design in order to reduce nozzle damage and degradation of the gas density
profile. Interferometric measurements showed that the J2021 had a narrower,
denser gas profile along the laser axis than the S900 nozzle. They also
revealed that He gas produced denser wings and broader density peaks than N2
or the He-N2 mix. J2021 and S900 nozzles will hereafter be referred to as
“short-” and “long-focus” nozzles, respectively.

Figure 4: Images corresponding to optical probe arrival $\sim 150$ ps after
the drive laser in a He gas with a long-focus shock nozzle (a) Raw
interferogram (b) Density map showing a plasma channel straddling the peak
density region at $x=250$ $\mu$m. The laser focus position in the vacuum was
set at $x=0$ $\mu$m.

To measure the electron density in the plasma channel, a folding-wave
interferometer was used to take optical interferograms of the ionised gas at
different temporal delays relative to the drive laser [53]. Fig. 4b shows a He
density distribution from the experiment taken $\simeq 150$ ps after the
arrival of the laser, revealing a laser channel with average radius $\simeq
70\leavevmode\nobreak\ \mu$m. Modelling the expansion as a Sedov-Taylor
cylindrical blast wave [54, 55], $R(t)=\xi_{0}(\mathcal{E}_{b}t^{2}/\rho_{\rm
gas}l_{p})^{1/4}$ gives an energy of $\mathcal{E}_{b}\simeq 1.3$ J (taking
$\xi_{0}=0.9$ [55]) deposited in the channel over its length of $l_{p}\simeq
0.5$ mm, which is less than 20% the deposited laser energy of 7.3 J. Such a
significant difference is explained by the fact that the expanding plasma is
essentially collisionless. Plasma ions propagate through the ambient gas and
ionise atoms without creating a density compression - only a small portion of
the slow ion population contribute to shock wave formation.

2D PIC simulations and experimental interferograms of the gas at the point of
laser arrival suggest that, by the time the laser has travelled through the
low-density wings of the gas density profile and arrived in the central high-
density region, the laser has become significantly defocused. For a gas
density of 4.5 bar and a plasma channel radius of $20\leavevmode\nobreak\
\mu$m, the plasma volume is $\sim 6\times 10^{-7}$ cm3, the laser energy
deposited in the gas is 7.3 J, the bulk electron temperature is $T_{e}\simeq
77$ keV and the pressure is 60 Mbar (see Tab. 1).

The stopping power of 77 keV electrons in He is $\sim 10$ MeV cm2/g [40],
which corresponds to a mean free path $\sim 30$ cm for our gas density. The
Debye radius, however, is of order $0.1\leavevmode\nobreak\ \mu$m, so bulk
electrons remain in the plasma due to the Coulomb attraction. Plasma expansion
is therefore quasi-neutral and Sedov’s self-similar solution for the shock
wave applies. Bremsstrahlung losses are negligible on this timescale, so the
plasma expands adiabatically.

Assuming that all bulk electron energy is transferred to ions, the average
energy of helium ions is about 2320 keV, their velocity is $3\,\mu$m/ps and
the expansion time is 150 ps. In this experiment, about 10% of the absorbed
laser energy is transferred to hot electrons with an effective temperature of
$\sim$1.1 MeV given by the ponderomotive scaling. Then using the plasma
charging model described in Sec. II, we estimate a plasma capacitance of
0.0086 pF, a plasma potential of 4.4 MV and 42 nC charge of escaped electrons.
The plasma electrostatic energy is about 0.1 J and the escaped electrons have
carried away 0.15 J.

Applying the analysis of gas ionisation described in Sec. II, we find that the
photoionisation probability is very low - about $1.6\times 10^{-7}$ \- the
level of ionisation by fast electrons is two orders of magnitude larger at
$\sim 3.3\times 10^{-5}$ and the dominant ionisation processes are electrical
breakdown and ions in the expanding plasma. The plasma ionisation time is
therefore within a few tens of ps. The plasma discharge results in EMP
emission with energy $\sim$0.17 mJ, which corresponds to an electric field of
$\sim 6.3$ kV/m and a magnetic field of $21\,\mu$T at 1 m from the source.
Nozzle damage is due to energy deposition of a few joules by the plasma ions.

Figure 5: Interferograms of the VEGA-3 laser interacting with an N2 gas
ejected from a short-focus shock nozzle at different probe times relative to
the arrival of the pump beam: (a) Probe time $t\sim 40$ ps (b) Probe time
$t\sim 90$ ps.

Progress of gas ionisation between the laser and nozzle was measured with a
$2\omega$ pick-off beam directed transversely to the laser channel for
interferometric imaging. Fig. 5 shows interferograms taken at two different
times after the arrival of the laser pulse. The gas is N2. Figure 5(a)
corresponds to the earliest probing time measured after the laser pulse
arrival at $t=0$ ps. The shadow of the gas is visible in both images,
suggesting that the entire gas volume can be ionised within 40 ps. The speed
of the ionisation front therefore exceeds $\sim 20\,\mu$m/ps, which is
consistent with gas ionisation by electrical breakdown.

To monitor ion emission during the experiment, five diamond time-of-flight
detectors [56] were placed in multiple different locations around the vacuum
chamber ($0^{\circ}$, $\pm 17^{\circ}$, $4.85^{\circ}$, $5.5^{\circ}$ with
respect to the laser axis, always inclined at $9^{\circ}$ to the horizontal
plane of the laser) and a Thomson parabola spectrometer was placed along the
laser axis in the same horizontal plane as the laser. When the diamond
detectors were placed at $\pm 17^{\circ}$, nitrogen ions with energy up to
$\sim 80$ MeV were measured. For shots on He gas, $\alpha$-particles were
accelerated to 0.7 MeV/u with $10^{9}$ particles per steradian, while shots on
N2 gas produced ions up to 5.7 MeV/u with $10^{7}$ particles per steradian.
These ions were measured in the laser forward direction (within a $\pm
17^{\circ}$ cone)[51].

###  VI.2 EMP Experiment on VEGA-3

A second experiment was conducted on VEGA-3 with a view to characterising the
EMP and ions produced in laser-gas interactions. The laser energy before
compressor was $\sim 30$ J and the pulse duration was 30 fs. Based on images
of the focal spot taken at low energy, 21% of the energy on-target was
contained within the first Airy disk[50] for an on-target intensity of order
$\sim 10^{20}$ W cm-2 at best compression, similar to the intensity reported
for the experiment in the previous section. The laser contrast was $10^{-12}$
with no pre-pulses. A Prodyn RB-230(R) radiation-hardened B-dot probe was used
to measure the amplitude of the magnetic field at different distances from the
gas jet, while two diamond time of flight detectors and a Thomson parabola
were used to monitor charged particle emission. Signal degradation due to EMP
pick-up in the unshielded oscilloscope prevented the easy identification of a
photo-peak in the time of flight data, so quantitative analysis of the ion
spectrum is not possible. B-dot signals were recorded on a Rohde&Schwarz RTO64
digital oscilloscope with 2 GHz bandwidth and 10 GS/s sample rate. The B-dot
probe was oriented so that its axis was parallel to the ground and sensitive
to an azimuthal magnetic field relative to the nozzle axis.

B-dot voltage signals were bandpass-filtered between 0.4 GHz and 2 GHz, with
the lower limit determined by the probe frequency response [57, 58] and the
upper limit by the oscilloscope bandwidth. The waveforms were then cropped,
the zero-point offset removed, and cable attenuation corrected in the Fourier
domain. The cable attenuation functions were measured using a Rohde&Schwarz
ZNA4 Vector Network analyser from 5 MHz to 4 GHz, but the correction was only
applied between 0.4 GHz and 2 GHz to avoid amplifying noise beyond the
sensitivity range of the diagnostic. Finally, the voltages were integrated in
time and multiplied by the probe effective area of 0.2 cm2 (supplied by the
manufacturer) to yield the magnetic field.

Figure 6: 3D graphic of the gas jet nozzle and solenoid valve assembly at
VEGA-3. Arrows indicate dimensions relevant to electromagnetic emission.

Both solid and gaseous targets were studied during the experiment. The gas was
a 3:97 H2-He mix at $\sim 1000$ bar backing pressure, forced vertically
downwards through the nozzle aperture to the laser focus. On shots with solid
targets, the nozzle and solenoid valve assembly (Fig. 6) was replaced by a
bracket and multi-foil array. The foils were made from $6\leavevmode\nobreak\
\mu$m-thick aluminium. Figure 7 shows typical EMP waveforms for solid and
gaseous targets, demonstrating a reduction by a factor $2-3$ in the peak
magnetic field for the same laser parameters when solid targets were switched
to gas. This is consistent with the results of Kugland et al. [8] on the
PHELIX laser with an Ar gas jet and tallies with our theoretical estimates.
The ChoCoLaT2 code [59] evaluates the charge produced by the VEGA-3 laser
interacting with $6\leavevmode\nobreak\ \mu$m-thick Al foils to be of order
100 nC, which is twice higher than the 42 nC estimated for a gas in Sec. VI.1.

Figure 7: Comparison of EMP waveforms for solid and gaseous targets on VEGA-3.
The signals were measured using a Prodyn RB-230(R) probe positioned at
$60^{\circ}$ to the laser forward direction at a horizontal distance of $2.66$
m from the nozzle and vertically in-line with the laser focal spot. The
maximum amplitude of the magnetic field was a factor $2-3$ times lower for the
gas targets compared to $6\leavevmode\nobreak\ \mu$m-thick solid Al foils.
Figure 8: Variation of EMP maximum magnetic field with distance from the gas
jet. Data was collected with the B-dot probe positioned at $\phi=60^{\circ}$
to the laser axis, with line of sight to the target occluded. The fitted curve
is for a $3$ cm-tall antenna with the angle between the antenna axis and the
probe assumed constant at $\theta=90^{\circ}$ for the different distances.

####  VI.2.1 Comparison with EMP Emission Model

Figure 8 shows measurements of the decay of the magnetic field with distance
from the gas jet. The data points come from experimental measurements and
represent the average of the maximum and minimum magnetic field values in the
waveform. Error bars represent one standard deviation from the mean. The green
points represent data taken when the B-dot was positioned at $60^{\circ}$ to
the laser axis, outside the vacuum chamber and behind a glass window. A
Thomson parabola spectrometer inside the chamber blocked the probe’s direct
line of sight to the target.

The magnitude of the magnetic field is of order $5-10\,\mu$T at a distance of
$\sim 2$ m from the jet. Significant shot-to-shot variations are due to
adjustments in the laser focal position inside the gas to optimise the laser
coupling to the target. There are insufficient data points to identify an
unambiguous scaling with distance, but they can allow us to estimate the
charge accumulated in the gas by the laser ejection of hot electrons if we
assume a dipolar radiation field. The solid line represents a least squares
fit to the data points with Eq. (1) from Ref. [46], assuming an antenna height
of $h=3$ cm (consistent with the vertical height of the jet nozzle in Fig. 6)
and leaving the target charge $Q$ as a free parameter. The best-fit charge is
$\sim 20$ nC in this case. This is in agreement with the model presented in
Sec. II, which predicts a charge of $\sim 40$ nC for the VEGA-3 experimental
conditions.

Peaks in the EMP Fourier spectrum constrain the EMP emission mechanism. The
average of the EMP Fourier spectra for shots with the gas jet targets reveals
multiple prominent resonances between $\nu_{\rm emp}\sim 1.2$ GHz and 1.9 GHz
(not shown here). Assuming antenna emission from a monopole of height
$c/4\nu_{\rm emp}$, the strongest resonances correspond to heights of $\sim
4-5$ cm - similar to the dimensions of the nozzle. Note that our measurements
were only sensitive to emissions from 0.4 GHz to 2 GHz, and there were other
large metallic objects in the chamber that might contribute to the EMP.

##  VII Conclusions

We have explored various mechanisms of gas ionisation and nozzle damage in
laser-gas interactions. Depending on the gas density and plasma temperature,
an electrical discharge and EMP will be triggered either by plasma expansion
from the laser focus or electrical breakdown of the ambient gas. The
relatively small plasma volume produced in laser-gas interactions leads to a
small plasma capacitance and this in turn produces a smaller ejected charge
and lower level of EMP compared to solid targets. Nozzle damage is caused by
plasma ions depositing energy in the nozzle surface rather than Ohmic heating
from the discharge current. Two experiments on the VEGA-3 laser have provided
useful supporting evidence for our model. The minimum speed of gas ionisation
- inferred from optical interferometry - is consistent with collisional
ionisation by ions in an expanding plasma or with the electric discharge.

Further dedicated experiments are needed to confirm the model presented in
this paper, in particular by measuring the emitted ion and electron spectra
over a large solid angle. Measuring the average ion energy will allow us to
estimate the discharge time and plasma expansion velocity. It is also
important to measure the laser-ejected charge since 10 times more hot
electrons imply 10 times stronger EMP fields. Direct measurement of a
discharge current in the nozzle and characterisation of the EMP field
structure is essential to confirm that the EMP is related to antenna emission
from the nozzle rather than large-scale plasma oscillations or chamber
resonant modes [6, 60].

Experimental validation of the nozzle damage mechanism requires measurement of
the ion energy distribution in the radial direction, in the energy range below
1 MeV. This might also be combined with a study of laser damage as the laser
is focused at various different heights above the gas nozzle. Switching from
metallic to ceramic nozzles would be useful for assessing the impact of nozzle
material.

###### Acknowledgements.

The authors would like to thank the staff at the VEGA-3 Laser Facility for
their hard work over the course of several experiments. This work has been
carried out within the framework of the EUROfusion Consortium, funded by the
European Union via the Euratom Research and Training Programme (Grant
Agreement No. 101052200 — EUROfusion). Views and opinions expressed are,
however, those of the authors only and do not necessarily reflect those of the
European Union or the European Commission. Neither the European Union nor the
European Commission can be held responsible for them. We acknowledge GENCI for
providing us access to the Joliot-Curie supercomputer (grants 2021-A0130512993
and 2022-A0130512993). We also acknowledge Grant PID2021-125389OA-I00, funded
by MCIN/ AEI / 10.13039/501100011033 / FEDER, UE and “ERDF A way of making
Europe”, funded by the European Union. V. Ospina-Bohórquez and C. Vlachos
acknowledge support from the LIGHT S&T Graduate Program (PIA3 Investment for
the Future Program, ANR-17-EURE-0027). This work received funding from the
European Union’s Horizon 2020 research and innovation program through the
European IMPULSE project under grant agreement No 871161 and from LASERLAB-
EUROPE V under grant agreement No 871124. It is published as part of the
international project “PMW”, co-financed by the Polish Ministry of Science and
Higher Education within the framework of the scientific financial resources
for 2021-2022 under the contract no 5205/CELIA/2021/0 (project CNRS no
239915).

## References

  * [1] C. Méndez, O. Varela, E. García, I. Hernández, J. Ajates, J.D. Pisonero, J.L. Sagredo, M. Olivar, and L. Roso.  Vega laser facility beamlines management for pump-probe experiments.  In Fourth Int. Conf. Applications of Optics and Photonics, volume 11207, page 431. SPIE, 2019.
  * [2] J. L. Dubois, F. Lubrano-Lavaderci, D. Raffestin, J. Ribolzi, J. Gazave, A. Compant La Fontaine, E. D’Humières, S. Hulin, Ph. Nicolaï, A. Poyé, and V. T. Tikhonchuk.  Target charging in short-pulse-laser-plasma experiments.  Phys. Rev. E, 89:1, 2014.
  * [3] F. Consoli, V. T. Tikhonchuk, M. Bardon, P. Bradford, D. C. Carroll, J. Cikhardt, M. Cipriani, R. J. Clarke, T. E. Cowan, C. N. Danson, R. De Angelis, M. De Marco, J.-L. Dubois, B. Etchessahar, A. L. Garcia, D. I. Hillier, A. Honsa, W. Jiang, V. Kmetik, J. Krasa, Y. Li, F. Lubrano, P. McKenna, A. Poye, I. Prencipe, P. Raczka, R. A. Smith, R. Vrana, N. C. Woolsey, E. Zemaityte, Y. Zhang, Z. Zhang, B. Zielbauer, and D. Neely.  Laser produced electromagnetic pulses: generation, detection and mitigation.  High Power Laser Sci. Eng., 8:e22, 2020.
  * [4] D. C. Eder, A. Throop, C. G. Brown, Jr., J. Kimbrough, M. L. Stowell, D. A. White, P. Song, N. Back, A. MacPhee, H. Chen, W. DeHope, Y. Ping, B. Maddox, J. Lister, G. Pratt, T. Ma, Y. Tsui, M. Perkins, D. O’Brien, and P. Patel.  Mitigation of electromagnetic pulse (EMP) effects from short-pulse lasers and fusion neutrons.  Lawrence Livermore National Laboratory Report, LLNL-TR-411183, 3 2009.
  * [5] Brown, C. G., Clancy, T. J., Eder, D. C., Ferguson, W., and Throop, A. L.  Analysis of electromagnetic pulse (EMP) measurements in the National Ignition Facility’s target bay and chamber.  EPJ Web of Conf., 59:08012, 2013.
  * [6] M. J. Mead, D. Neely, J. Gauoin, R. Heathcote, and P. Patel.  Electromagnetic pulse generation within a petawatt laser target chamber.  Rev. Sci. Instrum., 75:4225, 2004.
  * [7] A. Poyé, J. L. Dubois, F. Lubrano-Lavaderci, E. D’Humières, M. Bardon, S. Hulin, M. Bailly-Grandvaux, J. Ribolzi, D. Raffestin, J. J. Santos, Ph. Nicolaï, and V. Tikhonchuk.  Dynamic model of target charging by short laser pulse interactions.  Phys. Rev. E, 92:043107, 2015.
  * [8] N. L. Kugland, B. Aurand, C. G. Brown, C. G. Constantin, E. T. Everson, S. H. Glenzer, D. B. Schaeffer, A. Tauschwitz, and C. Niemann.  Demonstration of a low electromagnetic pulse laser-driven argon gas jet x-ray source.  Appl. Phys. Lett., 101:024102, 2012.
  * [9] M. Ehret and L. Volpe.  EMP measurements at VEGA - status and prospects, in the framework of the European IMPULSE project.  In 5th Electromagnetic Pulse Workshop at ECLIM, 2022.
  * [10] C. N. Danson, C. Häfner, J. Bromage, T. Butcher, J.-C. F. Chanteloup, E. A. Chowdhury, A. Galvanauskas, L. A. Gizzi, J. Hein, D. I. Hillier, N. W. Hopps, Y. Kato, E. A. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. H. Nam, D. Neely, D. Papadopoulos, R. R. Penman, L. Qian, J. J. Rocca, A. A. Shaykin, C. W. Siders, C. Spindloe, S. Szatmári, R. M. G. M. Trines, J. Zhu, P. Zhu, and J. D. Zuegel.  Petawatt and Exawatt class lasers worldwide.  High Power Laser Sci. Eng., 7:e54, 2019.
  * [11] K. L. Lancaster, S. Karsch, H. Habara, F. N. Beg, E. L. Clark, R. Freeman, M. H. Key, J. A. King, R. Kodama, K. Krushelnick, K. W. D. Ledingham, P. McKenna, C. D. Murphy, P. A. Norreys, R. Stephens, C. Stöeckl, Y. Toyama, M. S. Wei, and M. Zepf.  Characterization of Li7(p,n)7Be neutron yields from laser produced ion beams for fast neutron radiography.  Phys. Plasmas, 11:3404, 2004.
  * [12] P. K. Patel, A. J. Mackinnon, M. H. Key, T. E. Cowan, M. E. Foord, M. Allen, D. F. Price, H. Ruhl, P. T. Springer, and R. Stephens.  Isochoric heating of solid-density matter with an ultrafast proton beam.  Phys. Rev. Lett., 91:125004, 2003.
  * [13] K. Nemoto, A. Maksimchuk, S. Banerjee, K. Flippo, G. Mourou, D. Umstadter, and V. Yu. Bychenkov.  Laser-triggered ion acceleration and table top isotope production.  Appl. Phys. Lett., 78:595, 2001.
  * [14] A. Yogo, T. Maeda, T. Hori, H. Sakaki, K. Ogura, M. Nishiuchi, A. Sagisaka, H. Kiriyama, H. Okada, S. Kanazawa, T. Shimomura, Y. Nakai, M. Tanoue, F. Sasao, P. R. Bolton, M. Murakami, T. Nomura, S. Kawanishi, and K. Kondo.  Measurement of relative biological effectiveness of protons in human cancer cells using a laser-driven quasimonoenergetic proton beamline.  Appl. Phys. Lett., 98:053701, 2011.
  * [15] A. Macchi, M. Borghesi, and M. Passoni.  Ion acceleration by superintense laser-plasma interaction.  Rev. Mod. Phys., 85:751, 2013.
  * [16] M. S. Wei, S. P. D. Mangles, Z. Najmudin, B. Walton, A. Gopal, M. Tatarakis, A. E. Dangor, E. L. Clark, R. G. Evans, S. Fritzler, R. J. Clarke, C. Hernandez-Gomez, D. Neely, W. Mori, M. Tzoufras, and K. Krushelnick.  Ion acceleration by collisionless shocks in high-intensity-laser–underdense-plasma interaction.  Phys. Rev. Lett., 93:155003, 2004.
  * [17] J. C. Wood, D. J. Chapman, K. Poder, N. C. Lopes, M. E. Rutherford, T. G. White, F. Albert, K. T. Behm, N. Booth, J. S. J. Bryant, P. S. Foster, S. Glenzer, E. Hill, K. Krushelnick, Z. Najmudin, B. B. Pollock, S. Rose, W. Schumaker, R. H. H. Scott, M. Sherlock, A. G. R. Thomas, Z. Zhao, D. E. Eakins, and S. P. D. Mangles.  Ultrafast imaging of laser driven shock waves using betatron x-rays from a laser wakefield accelerator.  Sci. Rep., 8:11010, 2018.
  * [18] F. S. Tsung, R. Narang, W. B. Mori, C. Joshi, R. A. Fonseca, and L. O. Silva.  Near-GeV-energy laser-wakefield acceleration of self-injected electrons in a centimeter-scale plasma channel.  Phys. Rev. Lett., 93:185002, 2004.
  * [19] M. Barberio and P. Antici.  Laser-PIXE using laser-accelerated proton beams.  Sci. Rep., 9:6855, 2019.
  * [20] K. Ta Phuoc, S. Corde, C. Thaury, V. Malka, A. Tafzi, J.-P. Goddet, R.C. Shah, S. Sebban, and A. Rousse.  All-optical compton gamma-ray source.  Nat. Photon., 6:308, 2012.
  * [21] C.N. Danson, P.A. Brummitt, R.J. Clarke, J.L. Collier, B. Fell, A.J. Frackiewicz, S. Hancock, S. Hawkes, C. Hernandez-Gomez, P. Holligan, M.H.R. Hutchinson, A. Kidd, W.J. Lester, I.O. Musgrave, D. Neely, D.R. Neville, P.A. Norreys, D.A. Pepler, C.J. Reason, W. Shaikh, T.B. Winstone, R.W.W. Wyatt, and B.E. Wyborn.  Vulcan petawatt—an ultra-high-intensity interaction facility.  Nucl. Fusion, 44:S239, 2004.
  * [22] C.N. Danson, P.A. Brummitt, R.J. Clarke, J.L. Collier, B. Fell, A.J. Frackiewicz, S. Hawkes, C. Hernandez-Gomez, P. Holligan, M.H.R. Hutchinson, and et al.  Vulcan petawatt: Design, operation and interactions at $5\times 10^{20}$ W cm-2.  Laser Part. Beams, 23(1):87, 2005.
  * [23] V. Ospina-Bohórquez.  Ion acceleration from high-intensity laser interactions with quasi-critical-gas targets: experiments and numerical simulations.  PhD thesis, Université de Bordeaux; Universidad de Salamanca (Espagne). Facultad de ciencias, 2022.  Available at https://theses.hal.science/tel-04011154.
  * [24] V. Ospina-Bohórquez et al.,.  Laser-driven ion and electron acceleration from near-critical density gas targets: towards high-repetition rate operation in the 1 PW, sub-100 fs laser interaction regimes.  ArXiv.2311.04187, (1), 2023.
  * [25] G. S. Hicks, O. C. Ettlinger, M. Borghesi, D. C. Carroll, R. J. Clarke, E.-J. Ditter, T. P. Frazer, R. J. Gray, A. McIlvenny, P. McKenna, C. A. J. Palmer, L. Willingale, and Z. Najmudin.  Spectrally peaked proton beams shock accelerated from an optically shaped overdense gas jet by a near-infrared laser.  ArXiv.2104.13977, (1), 2021.
  * [26] J. Bonvalet, P. Loiseau, J.-R. Marquès, E. Atukpor, E. d’Humières, J. Domange, P. Forestier-Colleoni, F. Hannachi, L. Lancia, D. Raffestin, M. Tarisien, V. Tikhonchuk, and Ph. Nicolaï.  Laser-driven collisionless shock acceleration of protons from gas jets tailored by one or two nanosecond beams.  Phys. Plasmas, 28(11):113102, 2021.
  * [27] F. Sylla, A. Flacco, S. Kahaly, M. Veltcheva, A. Lifschitz, V. Malka, E. d’Humières, I. Andriyash, and V. Tikhonchuk.  Short intense laser pulse collapse in near-critical plasma.  Phys. Rev. Lett., 110:085001, 2013.
  * [28] A. Debayle, F. Mollica, B. Vauzour, Y. Wan, A. Flacco, V. Malka, X. Davoine, and L. Gremillet.  Electron heating by intense short-pulse lasers propagating through near-critical plasmas.  New J. Phys., 19:123013, 2017.
  * [29] I. M. Vladisavlevici, D. Vizman, and E. d’Humières.  Theoretical investigation of the interaction of ultra-high intensity laser pulses with near critical density plasmas.  Plasma Phys. Control. Fusion, 65:045012, 2023.
  * [30] K. Krushelnick, E. L. Clark, Z. Najmudin, M. Salvati, M. I. K. Santala, M. Tatarakis, A. E. Dangor, V. Malka, D. Neely, R. Allott, and C. Danson.  Multi-mev ion production from high-intensity laser interactions with underdense plasmas.  Phys. Rev. Lett., 83:737, 1999.
  * [31] L. Willingale, S. P. D. Mangles, P. M. Nilson, R. J. Clarke, A. E. Dangor, M. C. Kaluza, S. Karsch, K. L. Lancaster, W. B. Mori, Z. Najmudin, J. Schreiber, A. G. R. Thomas, M. S. Wei, and K. Krushelnick.  Collimated multi-mev ion beams from high-intensity laser interactions with underdense plasma.  Phys. Rev. Lett., 96:245002, 2006.
  * [32] S. C. Wilks, W. L. Kruer, M. Tabak, and A. B. Langdon.  Absorption of ultra-intense laser pulses.  Phys. Rev. Lett., 69:1383, 1992.
  * [33] F. F. Chen.  Introduction to Plasma Physics and Controlled Fusion.  Number v. 1. Springer, 1984.
  * [34] R. A. Simpson, G. G. Scott, D. Mariscal, D. Rusby, P. M. King, E. Grace, A. Aghedo, I. Pagano, M. Sinclair, C. Armstrong, M. J.-E. Manuel, A. Haid, K. Flippo, L. Winslow, M. Gatu-Johnson, J. A. Frenje, D. Neely, S. Kerr, G. J. Williams, S. Andrews, R. Cauble, K. Charron, R. Costa, B. Fischer, S. Maricle, B. Stuart, F. Albert, N. Lemos, A. Mackinnon, A. MacPhee, A. Pak, and T. Ma.  Scaling of laser-driven electron and proton acceleration as a function of laser pulse duration, energy, and intensity in the multi-picosecond regime.  Phys. Plasmas, 28:013108, 2021.
  * [35] P. Mora.  Plasma expansion into a vacuum.  Phys. Rev. Lett., 90:185002, 2003.
  * [36] M. Murakami and M. M. Basko.  Self-similar expansion of finite-size non-quasi-neutral plasmas into vacuum: Relation to the problem of ion acceleration.  Phys. Plasmas, 13:012105, 2006.
  * [37] K. I. Popov, V. Yu. Bychenkov, W. Rozmus, and L. Ramunno.  A detailed study of collisionless explosion of single and two-ion-species spherical nanoplasmas.  Phys. Plasmas, 17:083010, 2010.
  * [38] A. S. Richardson.  2019 NRL plasma formulary.  Naval Research Laboratory Washington, DC, 2019.
  * [39] W.-M. Yao et al.  Review of particle physics.  J. Phys. G: Nuclear and Particle Physics, 33:1, 2006.
  * [40] NIST Physics Reference Data.  https://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html.
  * [41] V. Chepel and H. Araújo.  Liquid noble gas detectors for low energy particle physics.  J. Instrumentation, 8:R04001, 2013.
  * [42] V. T. Tikhonchuk.  Interaction of a beam of fast electrons with solids.  Phys. Plasmas, 9:1416, 2002.
  * [43] NIST Physics Reference Data.  https://physics.nist.gov/PhysRefData/Star/Text/PSTAR.html.
  * [44] U. Giesen and J. Beck.  New measurements of W-values for protons and alpha particles.  Radiation Protection Dosimetry, 161:23, 2014.
  * [45] W.Y. Baek and B. Grosswendt.  Energy Dependence of W Values for Protons in Gases.  Radiation Protection Dosimetry, 52:97, 1994.
  * [46] D. F. G. Minenna, A. Poyé, P. Bradford, N. Woolsey, and V. T. Tikhonchuk.  Electromagnetic pulse emission from target holders during short-pulse laser interactions.  Phys. Plasmas, 27:063102, 2020.
  * [47] M. Bardon, B. Etchessahar, F. Lubrano, S. Bazzoli, M. Ferri, J. Ribolzi, P. Mirabel, A. Compant La Fontaine, N. Mallejac, S. Cadra, L. Chaigne, S. Depierreux, J. Baggio, N. Blanchot, G. Birindelli, A. Casner, and V. T. Tikhonchuk.  Mitigation of strong electromagnetic pulses on the LMJ-PETAL facility.  Phys. Rev. Res., 2:033502, 2020.
  * [48] NIST.  Silicon Carbide, WebBook de Chimie NIST, srd 69.  https://webbook.nist.gov/cgi/cbook.cgi?ID=C409212&Units=SI&Mask=FFFF&Type=JANAFS&Table=on.  Accessed: 10-12-2022.
  * [49] J. F. Ziegler and J. P. Biersack.  The stopping and range of ions in matter.  http://www.srim.org/index.htm#HOMETOP.  Accessed: 10-12-2022.
  * [50] J. L. Henares, P. Puyuelo-Valdes, C. Salgado-López, J. I. Apiñaniz, P. W. Bradford, F. Consoli, D. de Luis, M. Ehret, F. Hannachi, R. Hernández-Martín, A. Huber, L. Lancia, M. Mackeviciute, A. Maitrallain, J.-R. Marquès, J.A. Pérez-Hernández, C. Santos, J. J. Santos, V. Stankevic, M. Tarisien, V. Tomkus, L. Volpe, and G. Gatti.  Proton and helium ions acceleration in near-critical density gas targets by short-pulse Ti:Sa PW-class laser.  J. Instruments, 2023.
  * [51] V. Ospina-Bohórquez et al.,.  Laser-driven ion and electron acceleration from near-critical density gas targets: towards high-repetition rate operation in the 1 PW, sub-100 fs laser interaction regimes.  Phys. Rev. Research, 2024.
  * [52] J. L. Henares, P. Puyuelo-Valdes, F. Hannachi, T. Ceccotti, M. Ehret, F. Gobet, L. Lancia, J.-R. Marquès, J. J. Santos, M. Versteegen, and M. Tarisien.  Development of gas jet targets for laser-plasma experiments at near-critical density.  Rev. Sci. Instrum., 90:063302, 2019.
  * [53] T. Pisarczyk, J.J. Santos, R. Dudzak, A. Zaras-Szydłowska, M. Ehret, Z. Rusiniak, J. Dostal, T. Chodukowski, O. Renner, S.Yu. Gus’kov, Ph. Korneev, T. Burian, Ch. Vlachos, Iu. Kochetkov, D. Makaruk, M. Rosinski, M. Kalal, M. Krupka, M. Pfeifer, D. Klir, J. Cikhardt, J. Krasa, S. Singh, S. Borodziuk, M. Krus, L. Juha, J. Hrebicek, J. Golasowski, and J. Skala.  Elaboration of 3-frame complex interferometry for optimization studies of capacitor-coil optical magnetic field generators.  J. Instrumentation, 14:C11024, 2019.
  * [54] G. J. Hutchens.  Approximate cylindrical blast theory: Near‐field solutions.  J. Appl. Phys., 77:2912, 1995.
  * [55] Ya.B. Zeldovich and Yu.P. Raizer.  Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena.  Dover Publications, New York, 2002.
  * [56] M. Salvadori, F. Consoli, C. Verona, M. Cipriani, M. P. Anania, P. L. Andreoli, P. Antici, F. Bisesto, G. Costa, G. Cristofari, R. de Angelis, G. Di Giorgio, M. Ferrario, M. Galletti, D. Giulietti, M. Migliorati, R. Pompili, and A. Zigler.  Accurate spectra for high energy ions by advanced time-of-flight diamond-detector schemes in experiments with high energy and intensity lasers.  Sci. Rep., 11:3071, 2021.
  * [57] P. Ra̧czka, J.-L. Dubois, S. Hulin, V. Tikhonchuk, M. Rosiński, A. Zaraś-Szydłowska, and J. Badziak.  Strong electromagnetic pulses generated in high-intensity short-pulse laser interactions with thin foil targets.  Laser Part. Beams, 35:677, 2017.
  * [58] J. L. Dubois, P. Ra̧czka, S. Hulin, M. Rosiński, L. Ryć, P. Parys, A. Zaraś-Szydłowska, D. Makaruk, P. Tchórz, J. Badziak, J. Wołowski, J. Ribolzi, and V. Tikhonchuk.  Experimental demonstration of an electromagnetic pulse mitigation concept for a laser driven proton source.  Rev. Sci. Instrum., 89:103301, 2018.
  * [59] A. Poyé, S. Hulin, J. Ribolzi, M. Bailly-Grandvaux, F. Lubrano-Lavaderci, M. Bardon, D. Raffestin, J. J. Santos, and V. Tikhonchuk.  Thin target charging in short laser pulse interactions.  Phys. Rev. E, 98:033201, 2018.
  * [60] F. Consoli, P. L. Andreoli, M. Cipriani, G. Cristofari, R. De Angelis, G. Di Giorgio, L. Duvillaret, J. Krása, D. Neely, M. Salvadori, M. Scisciò, R. A. Smith, and V. T. Tikhonchuk.  Sources and space-time distribution of the electromagnetic pulses in experiments on inertial confinement fusion and laser-plasma acceleration.  Phil. Trans. Royal Soc. A, 379(2189):20200022, 2021.


# Examining Lower Latency Routing with Overlay Networks

Aakriti Kedia
<EMAIL_ADDRESS>
Akhilan Ganesh
<EMAIL_ADDRESS>
Aman Aggarwal
<EMAIL_ADDRESS>

###### Abstract

In today’s rapidly expanding digital landscape, where access to timely online
content is paramount to users, the underlying network infrastructure and
latency performance significantly influence the user experience. We present an
empirical study of the current Internet’s connectivity and the achievable
latencies to propose better routing paths if available. Understanding the
severity of the non-optimal internet topology with RIPE Atlas stats, we
conduct practical experiments to demonstrate that local traffic from the San
Diego area to the University of California, San Diego reaches up to Los
Angeles before serving responses. We examine the traceroutes and build an
experimental overlay network to constrain the San Diego traffic within the
city to get better round-trip time latencies.

##  1 Introduction

The current Internet topology is a web of transit and peering connections
between numerous autonomous systems, which facilitate the high inter-
connectivity of the Internet. However, this inter-connectivity has certain
limitations. Since each autonomous system links up with the Internet on the
basis of minimum cost, many sub-optimal geographical and physical routing
paths are prioritized for the routing of general traffic.

The significance of Internet Exchange Points (IXPs) may play a role here. IXPs
are physical centers that facilitate peering connectivity between Internet
Service Providers (ISPs). Los Angeles (LA) has quite a few IXPs and these are
the ones closest to San Diego Datacenter Map . This means that any traffic
that must be transferred from one ISP to another in San Diego is likely to be
routed all the way through LA and back. The connectivity of the University of
California, San Diego (UCSD) network with respect to the San Diego area is a
direct consequence of this Internet setup. In reality, even while the UCSD
network and off-campus ISPs are geographically proximal, packets traveling to
and from off-campus users and on-campus servers will still be routed through
LA as shown in Figure 1.

Figure 1: Network path from outside UCSD within San Diego to UCSD ieng6
through LA IXP

This paper aims to (1) quantify the national severity of non-optimal
forwarding paths and disconnectivity, to explore potential lower-latency
overlays, (2) explore the topology involved when interacting with UCSD
resources from off-campus and confirm the presence of LA IXP in the routing
path, and (3) experiment with an overlay network to bypass the LA IXP and
reduce effective latency of local UCSD traffic.

##  2 Background and Related Work

An overlay network is a network built on an already existing underlay network
infrastructure. The chain of physical or virtual underlay links between two
overlay nodes becomes a virtual overlay link on the overlay network Ding et
al. [2009]. Our research explores using overlay networks to gain better
performance compared to routing in an underlay network, similar in intent to
the role of resilient overlay networks which mitigate network faults Andersen
et al. [2001]. However, our research explores potential improvements in
latency rather than fault tolerance when using overlay networks to exploit or
transform the current topology of the Internet.

For our work, we specifically analyze RIPE Atlas data RIPE NCC , and
specifically keep in mind the findings of Holterbach et al. [2015] and Bajpai
et al. [2015]. As suggested in these papers, we remove noise wherever possible
and report only insights with at least $1\%$ improvement. We build on the
ideas of efficiency of geographic routing as stated in Sukhov and Onoprienko
[2014] and our results align with the findings of Subramanian et al. [2002]
where packets traveling through different ISPs encounter higher latencies. The
criteria and metrics used for reporting results uses the ping and traceroute
framework explained in Paxson et al. [1998]. We also refer to CAIDA - Center
for Applied Internet Data Analysis  datasets about connectivity and routing of
the global Internet.

##  3 Methodology

We quantify the severity of the non-optimal internet topology by rigorously
analyzing the publicly available global ping measurement stats provided by
RIPE Atlas. We also conduct a UCSD level experiment to examine the layer-3
routing topology and understand the general properties and problems of the
underlay network.

###  3.1 RIPE Atlas

We collect the ping stats from the measurement data provided by RIPE for all
measurements started after 1st January, 2023 till 19th May, 2023. Data cleanup
is performed by filtering only those measurements which are of stopped status
so that the ongoing and incomplete data do not bias the analysis.

RIPE has internal probes, which are network devices that are installed to get
network stats. Our analysis involved 10000 measurement ids with 11844 global
probes involved. We focus primarily on ipv4 ping latencies and keep probes
that collect only ipv6 data out of consideration. Under these constraints, we
collected 309959 loglines of data and analyze them to create every possible
triplet to see if it is possible to redirect data between any source node to a
destination node via a middle node but get a better latency compared to the
actual ping latency between the source node and the destination node obtained
from the measurement data from RIPE. We identify numerous insights about non-
optimal routing and internet disconnectivity as detailed in the 4.1 section.

To further understand the severity, we further drilled down our analysis to IP
level, which is a level deeper than RIPE probes, as a single RIPE probe
collects data for groups of ASes. The filtered measurements only include
”stopped” status and started after 1st March, 2023. Further, only ipv4 IPs
specific to the USA region are focused on to get a more holistic view of the
United States region. This leads to a subset of 10,000 measurement ids and
around 4212728 loglines of ping data consisting of 16756 unique ips. IP-info
online tool ipinfo.io  was used for mapping IP addresses to the corresponding
city, region, and state to further analyze these levels.

We account for noise in the data by using the median of the ping latency
available from the measurements. Each measurement sample from RIPE collects
ping latency in three test runs. We sort these runs and move forward with the
median of these. Further, data between source-destination pairs collected
across different measurements are averaged to minimize the possibility of
measurement data errors. We found some interesting insights which are detailed
further in 4.1

###  3.2 San Diego-UCSD Internet Analysis

We conduct a preliminary analysis of the Internet topology with respect to the
UCSD network. This is done via a hands-on internet measurement data collection
experiment of pings and traceroutes to ucsd.edu and ieng6.ucsd.edu from
diverse locations in and around the San Diego area and UCSD campus (Figure 2).
These include the following: UCSD CSE building (wifi), UCSD Geisel library
(wifi), San Diego downtown (AT&T wifi, Verizon, and AT&T), La Jolla downtown
(Spectrum wifi and AT&T), Miramar (Spectrum wifi and AT&T), and San Diego
airport SAN (AT&T wifi). We exploit both wifi and cellular networks to get
more robust results.

We log the ping and traceroute for each pair of source (associated with a
specific ISP) and destination. The Time-To-Live field of the ping response
indicates the number of hops that a packet takes to arrive at the destination
address. We cross-check this value with the number of hops observed from
traceroute analyis. Lastly, we record whether sources had packets routed to LA
at some point in the traceroute.

Figure 2: Ping and Traceroute sources to UCSD.

###  3.3 Designing and Testing a UCSD Bridge

We propose a 3-hop overlay network solution to route network traffic directly
to UCSD without being routed to an LA IXP. The overlay network would resemble
the design in Figure 3. The network nodes are as follows:

Node A:  A computer connected to a San Diego ISP. This node represents users
who want to retrieve UCSD resources (in this case, the ieng6 server) either
via the usual layer-3 routing or via the overlay network.

Node B:  A forwarding server that is connected on one port to a San Diego ISP
and connected on another port to the UCSD network. This node serves as a
network bridge that forwards packets through each network, allowing network
traffic to potentially bypass the LA IXP.

Node C:  The ieng6.ucsd.edu server hosted within the UCSD network. In a full
implementation of an overlay network, there could be multiple types of node C,
each hosting different resources on the UCSD network.

Figure 3: Proposed 3-node overlay network bypassing the LA IXP

We attempt to setup a network bridge connected to UCSD wifi and also connected
to the AT&T cellular network. It is posed as an Ethernet connection via USB
tethering. We used different ports for the Wifi and cellular network. We plan
to receive traffic on the cellular network port which can then be internally
forwarded to UCSD Wifi. However, on running the experiment we found that in
order to setup a reachable server through cellular we need administrative
privileges on the cellular network router. This is to override the Network
Address Translation (NAT) system in place and forward traffic to our specific
part on the experimental server. Lacking these privileges, we leave an actual
implementation of the overlay network and concrete design of node B for future
work. Instead, we collect measurements of the RTTs between each node to
simulate the expected latencies that such a network is expected to have.

For our simulation, we measure ping times between a device in AT&T cellular
network to another device in the same cellular network. We represent this ping
latency as the latency between node A and B. We collect another ping time
measurement between a device connected to UCSD wifi to indicate an on-campus
resource and an ieng6 server of UCSD, which is another resource within UCSD.
This represents the latency between node B and C. For our simulation, we
assume that the forwarding time between node B of the cellular network to node
B of the on-campus resource is minimal and we don’t consider it when reporting
results. So in our simulation, A-to-B resides on the AT&T cellular network,
while B-to-C resides on the UCSD network. For each ping measurement, 1000
packets were collected and the round trip times were compared for the
analysis.

Additionally, we analyze the traceroutes of each of these connections to gain
a better understanding of the routes that the proposed overlay network takes,
and whether it bypasses the LA IXP.

##  4 Results

The following results globally quantify the problem of non-optimality in
Internet topology and suggest alternate overlays for better connectivities and
latencies.

###  4.1 RIPE Atlas data analysis

From the experiments conducted on RIPE probes, we identified that Comcast
Business Gateway Router Type in the region of Illinois (Probe ID $10194$) has
no connectivity to New South Wales region of Australia (Probe ID $6636$). We
propose an overlay path via France using Bouygues Telecom SA ISP (Probe ID
$1003746$). The overlay latency is expected to be less than 5 ms as
illustrated in Figure 4. Illinois to France (city Paris) takes 0.3 ms and
France to Australia 4.6 ms.

Figure 4: Illinois and Australia via France

Similarly, Washington region of United States via the EMERALD-ONION ISP (Probe
ID $6934$) is connected to Australia (Probe ID $6636$) but lacks connectivity
to France (Probe ID $1003746$). An overlay path to France via Australia would
be 4.4ms as shown in Figure 5.

Figure 5: Seattle and France via Australia

Another interesting insight is the ping latency from SPACEX-STARLINK ISP,
Washington region (Probe ID $62498$) to Australia (Probe ID $6636$). The
current round-trip-time is 6.57ms but if forwarded via France using Bouygues
Telecom SA ISP (Probe ID $1003746$), an improvement of 0.81ms can be achieved.

We further drill down on IP level to discover that out of 108356 source IP,
destination IP combinations, 105479 combinations could show a ping latency
improvement of alteast $1\%$. Table 1 shows comprehensive quantitative
results. Although, a signicant number of combination pairs allow for $<10\%$
of ping latency improvement, there are also combinations which allow upto
$100\%$ improvements as depicted by Figure 6.

Figure 6: Ping percent improvements vs Source-destination pair counts percent_improvement | src_dst_pairs_count
---|---
1.0 | 5351
2.0 | 4939
3.0 | 4560
4.0 | 4121
5.0 | 3916
6.0 | 3533
7.0 | 3256
8.0 | 3061
9.0 | 2792
10.0 | 2450
Table 1: Ping percent improvements

One of our insights from IP data includes IPs in Milpitas don’t follow an
optimal path when directing traffic to IPs in the east US. The current ping
time between these IPs go upto as high as 265 ms. Cities like Phoenix,
Hilliard, Ashburn, San Francisco can form a lower latency overlay network
connecting Milpitas to the east. Figure 7 shows the current ping latency as
dashed line (265.49ms), and an optimal path in green of 65ms, giving an
improvement of 200ms. As the data is the median of three ping runs and is
averaged over all measurement samples, it is reflective of the topology
between Milpitas and Morrisdale following a high latency path.

Figure 7: Milpitas and Morrisdale via Las Cruces

Similarly, Figure 8 shows another example. Traffic from Newark to Las Cruces
takes 53.5ms but when directed through Kenett Square takes 6.25ms from Newark
to Kenett Square and 37.6ms from Kenett Square to Las Cruces.

Figure 8: Newark and Las Cruces via Kenett Square

However, all internet topology might not necessarily follow shortest paths.
Sometimes, distant servers might provide better latencies than those within
the same region. For example, Figure 9 shows that an optimal path of reaching
LA from Arroy Grande hits the east of US all the way to Appleton. This
indicates that some ISPs might have optimal latency servers deployed across
geographies or the path latencies might depend on the network congestions.

Figure 9: Arroy Grande to LA via Appleton

###  4.2 UCSD Network Analysis

During our traceroute analysis, we figured out that www.ucsd.edu was
externally hosted by Amazon AWS Global Accelerator servers, located in
Washington, U.S. Thus, we consider only ieng6.ucsd.edu as the on-campus
resource henceforth. Table 2 shows our experimental locations, the number of
hops and if the packets are routed through LA IXP.

Results confirm that almost all external traffic to the ieng6 resource is
routed through LA, which the UCSD experimental network bridge aims to address.
It further shows that sources within the UCSD network only travel 5 hops to
reach the ieng6 server, whereas the outside sources require at least 10 hops.

Experimental source | # Hops | LA IXP?
---|---|---
UCSD CSE wifi | 5 | No
UCSD Geisel wifi | 5 | No
SD Downtown wifi | 12 | Yes
SD Downtown Verizon | 18 | Yes
SD Downtown AT&T | 12 | Yes
LJ Downtown wifi | 14 | Yes
LJ Downtown AT&T | 16 | Yes
Miramar wifi | 14 | Yes
Miramar AT&T | 16 | Yes
SAN wifi | 15 | Unknown
Table 2: Number of hops and routing IXP for San Diego locations

Experimental results from the simulated overlay network are demonstrated in
Figure 11 (latency between node A and B), Figure 12 (latency between node B
and C), and Figure 10 (latency between node C and A). We consider ping
latencies as continuous values and plot the distributions for the measurements
between all pairs of nodes.

| Mean (ms) | Median (ms) | Variance (ms2) | Mode (ms) | Std Dev. (ms)
---|---|---|---|---|---
Ping between A and B | $57.451\,219\,512\,195\,124$ | $58.0$ | $159.085\,018\,837\,993\,2$ | $59$ | $12.612\,890\,978\,597\,777$
Ping between B and C | $10.466\,880\,566\,801\,635$ | $12.216\,999\,999\,999\,999$ | $11.510\,906\,220\,553\,505$ | $12.52$ | $3.392\,772\,644\,984\,262$
Ping between A and C via B | $67.918\,100\,079$ | $70.217$ | $170.595\,925\,058\,5$ | $71.52$ | $13.061\,237\,501$
Ping between A and C | $61.723\,446\,893\,787\,575$ | $62.0$ | $117.502\,676\,696\,077\,66$ | $61$ | $10.839\,865\,160\,419\,555$
Table 3: Summary statistics of ping time data for all the three routes - A and
B, B and C, and A and C - and aggregate of data from A and B and B and C to
predict that between A and C via B

As illustrated in Figure 10, the ping latencies between A and C follow a
unimodal distribution with an average ping latency of
$61.723\,446\,893\,787\,575$ and a median of $62.0$. These high statistics are
indicative of the traceroute results of traffic being routed from A to LA IXP
and then down to C as depicted in Figure 1. It’s interesting to note that the
standard deviation in this analysis is moderate (1̃6%) which can indicate some
congestion in the network.

Figure 10: Unimodal RTT frequency distribution from A to C

Figure 11 shows that the ping times distribution from A to B is also unimodal
but with a lower mean $57.451\,219\,512\,195\,124$ and median $58.0$ as
compared to route A to C. Traceroute analysis from A to B shows that the
packets are served within the San Diego network and hence have a round trip
time latency of $4ms$ lower compared to A to C. The difference $4ms$ is still
underwhelming as the route covers a lesser geographical distance (within San
Diego vs through LA). The standard deviation for this sample is
$12.612\,890\,978\,597\,777$ which indicates an instability in the network
which can be because of routing delays like queuing delay, propagation delay,
etc.

Figure 11: Unimodal RTT frequency distribution from A to B

As Figure 12 explains, distribution for ping times between B and C takes on a
bimodal distribution with first mode at $4ms$ and the second one at $12.52$,
with the second mode being significantly more frequent than the first. As it
is a bimodel distribution, the mean $10.466\,880\,566\,801\,635$ is not a good
representation of the central location of the data as it can be affected by
the two modes . Therefore, we rely on median ($12.216\,999\,999\,999\,999$
ms), a better estimate of the central tendency of the data. The standard
deviation for this distribution is $3.392\,772\,644\,984\,262$ ms which is
comparatively lower than the other two routes. This result aligns with our
expectations that route B to C should show better latencies as it is within
the internal UCSD network and can be transmitted with lesser number of hops.
Standard deviation of $3.392\,772\,644\,984\,262$ms with respect to the median
of $12.216\,999\,999\,999\,999$ms still conveys network instability.

Figure 12: Bimodal RTT frequency distribution from B to C

We combine the statistics of ping latencies from A to B with those from B to C
to represent the estimated latencies from A to C via an overlay through B. For
standard deviation, we add the two variances and then square-root the sum to
resemble the combined deviation. For all other metrics, we add the results
from A to B and from B to C.

Due to the bimodal distribution of ping times from B to C, mean is not a good
statistic for comparison 11. Therefore, we consider the mode or median to
compare the ping times from A to C directly versus through node B. Comparing
the medians, we observe that ping latency from A to C directly would be $8.22$
ms faster compared to the latency through B. Similarly, comparing the modes
reveals that latency from A to C directly is $10.52$ms faster than through B.

Though the results did not align with RIPE Atlas results of strategically
designed overlay networks yielding better latencies, future work in this
direction can still yield promising results. As our sample data was restricted
to only AT&T and UCSD ASes, the benefits of the overlay network were not
prominent. We further discovered that an AT&T router on the path from A to B
was located in LA, and therefore traffic was unavoidably being routed through
LA, which forfeits our assumption of the traffic between A and B being
constrained within San Diego. Additionally, as ASes are financially
incentivized to optimize for shortest-path routing, the simulated setup might
be able to propose improvements only when multiple ASes are involved and
transit relationships influence path forwarding.

##  5 Conclusion

Having rigorously analyzed the network topology using RIPE Atlas measurements,
we found great insights about the connectivity and the non-optimal latencies
between geographies. We further simulated a hands-on experiment to demonstrate
that local San Diego traffic is being routed to LA. Despite simulating the
experiment, we could not achieve an improvement in routing the local traffic
within San Diego due to lack of network administrative privileges and mobile
ISP routing going through LA. The RIPE Atlas results are promising and we
still believe that constraining traffic within San Diego would improve
latencies because UCSD on-campus pings to ieng6 yield much lower latencies
than off-campus pings. As future work, we aim to conduct the same experiment
on a larger scale with at least a million data points and a server that is
directly reachable within San Diego ISPs and that can also access the UCSD
network directly. We further consider wireless networks as a possibility of
network instability and hence conducting the experiment on wired systems can
also prove fruitful.

## References

  * [1] Datacenter Map.  Datacenter Map - Internet Exchange Points.  https://www.datacentermap.com/ixps.html.  Accessed: 2023-06-07.
  * Ding et al. [2009] Jianguo Ding, Ilangko Balasingham, and Pascal Bouvry.  Management of overlay networks: A survey.  In _2009 Third International Conference on Mobile Ubiquitous Computing, Systems, Services and Technologies_ , pages 249–255, 2009.  doi: 10.1109/UBICOMM.2009.49.
  * Andersen et al. [2001] D.G. Andersen, H. Balakrishnan, M.F. Kaashoek, and R. Morris.  The case for resilient overlay networks.  In _Proceedings Eighth Workshop on Hot Topics in Operating Systems_ , pages 152–157, 2001.  doi: 10.1109/HOTOS.2001.990076.
  * [4] RIPE NCC.  RIPE Atlas Legal.  https://atlas.ripe.net/legal/.  Accessed: .
  * Holterbach et al. [2015] Thomas Holterbach, Cristel Pelsser, Randy Bush, and Laurent Vanbever.  Quantifying interference between measurements on the ripe atlas platform.  In _Proceedings of the 2015 Internet Measurement Conference_ , IMC ’15, page 437–443, New York, NY, USA, 2015. Association for Computing Machinery.  ISBN 9781450338486.  doi: 10.1145/2815675.2815710.  URL https://doi.org/10.1145/2815675.2815710.
  * Bajpai et al. [2015] Vaibhav Bajpai, Steffie Jacob Eravuchira, and Jürgen Schönwälder.  Lessons learned from using the ripe atlas platform for measurement research.  _SIGCOMM Comput. Commun. Rev._ , 45(3):35–42, jul 2015.  ISSN 0146-4833.  doi: 10.1145/2805789.2805796.  URL https://doi.org/10.1145/2805789.2805796.
  * Sukhov and Onoprienko [2014] Andrei M. Sukhov and Artem V. Onoprienko.  Evaluating the effectiveness of geographic routing based on ripe atlas data.  In _2014 22nd Telecommunications Forum Telfor (TELFOR)_ , pages 107–110, 2014.  doi: 10.1109/TELFOR.2014.7034368.
  * Subramanian et al. [2002] Lakshminarayanan Subramanian, Venkata N Padmanabhan, and Randy H Katz.  Geographic properties of internet routing.  In _USENIX Annual Technical Conference, General Track_ , pages 243–259, 2002.
  * Paxson et al. [1998] Vern Paxson, Guy Almes, Jamshid Mahdavi, and Matt Mathis.  Framework for ip performance metrics.  Technical report, 1998.
  * [10] CAIDA - Center for Applied Internet Data Analysis.  The CAIDA macroscopic internet topology data kit.  https://www.caida.org/catalog/datasets/internet-topology-data-kit.  Accessed: 2023-06-09.
  * [11] ipinfo.io.  IPinfo JSON.  https://ipinfo.io/json.  Accessed: 2023-06-07.