Now at ]First Light Fusion Now at ]Shanghai Jiao Tong University Now at
]Lawrence Livermore National Laboratory

# Measurement of magnetic cavitation driven by heat flow in a plasma

C. Arran  Corresponding author  York Plasma Institute, Department of Physics,
University of York, YO10 5DD  P. Bradford  York Plasma Institute, Department
of Physics, University of York, YO10 5DD  G. S. Hicks  The John Adams
Institute for Accelerator Science, Blackett Laboratory, Imperial College
London, London SW7 2BZ, UK  S. Al-Atabi  The John Adams Institute for
Accelerator Science, Blackett Laboratory, Imperial College London, London SW7
2BZ, UK  L. Antonelli  York Plasma Institute, Department of Physics,
University of York, YO10 5DD  A. Dearling  York Plasma Institute, Department
of Physics, University of York, YO10 5DD  O. C. Ettlinger  The John Adams
Institute for Accelerator Science, Blackett Laboratory, Imperial College
London, London SW7 2BZ, UK  M. Khan  York Plasma Institute, Department of
Physics, University of York, YO10 5DD  M. P. Read  [  York Plasma Institute,
Department of Physics, University of York, YO10 5DD  K. Glize  [  Central
Laser Facility, STFC Rutherford Appleton Laboratory, Oxfordshire OX11 0QX, UK
M. Notley  Central Laser Facility, STFC Rutherford Appleton Laboratory,
Oxfordshire OX11 0QX, UK  C. A. Walsh  [  Blackett Laboratory, Imperial
College London, London SW7 2BZ, UK  R. J. Kingham  Blackett Laboratory,
Imperial College London, London SW7 2BZ, UK  Z. Najmudin  The John Adams
Institute for Accelerator Science, Blackett Laboratory, Imperial College
London, London SW7 2BZ, UK  C. P. Ridgers  York Plasma Institute, Department
of Physics, University of York, YO10 5DD  N. Woolsey  York Plasma Institute,
Department of Physics, University of York, YO10 5DD

###### Abstract

In extreme pressures and temperature gradients, heat flow and magnetic fields
are strongly coupled, but although theoretical work shows that strong heat
flows can cause significant changes in the magnetic field Biermann (1950);
Braginskii (1958); Haines (1986), it has long proven difficult to measure
these changes experimentally. Here we describe the first direct measurement of
Nernst-driven magnetic cavitation, in which heat flow causes expulsion of the
magnetic field from the hottest regions of a plasma. Using laser-driven proton
radiography Borghesi  _et al._ (2006), we demonstrate that Nernst advection
dominates changes to the magnetic field in underdense plasmas on these
nanosecond timescales. Due to the increased magnetic field strength at the
edge of the hot plasma, the observed magnetic cavitation can be accurately
described by fluid models of heat flow, despite mean free paths much longer
than the temperature gradient. Expulsion of the magnetic field from hot
regions of the plasma reduces the effectiveness of magnetised fusion
techniques Sefkow  _et al._ (2014) and disrupts magnetised plasma experiments.

The Nernst effect is familiar in semiconductors and has been measured in semi-
metals and even superconductors Behnia and Aubin (2016). In all of these
cases, mobile charge carriers in a temperature gradient are deflected by a
perpendicular magnetic field. The larger gyroradii and lower collision
frequency of particles at higher temperatures results in a net motion of
carriers perpendicular to both the temperature gradient and the magnetic
field, establishing an electric field. In plasmas, this is typically described
using classical transport theory by the thermal force acting on electrons as
$\bm{\mathrm{F}_{\perp}}\propto-\bm{\nabla}T_{e}\times\bm{\mathrm{B}}$
Braginskii (1958). When the Nernst electric field has a non-zero curl, the net
motion of charge carriers drives advection of the magnetic field as
$\partial\bm{\mathrm{B}}/\partial
t=\bm{\nabla}\times(\bm{\mathrm{v_{N}}}\times\bm{\mathrm{B}})$, where the
Nernst advection velocity is given by $\bm{\mathrm{v_{N}}}\approx
2\bm{\mathrm{\phi_{q}}}/5n_{e}T_{e}$ for a heat flow $\bm{\mathrm{\phi_{q}}}$
Nishiguchi  _et al._ (1984); Haines (1986). That is, the magnetic field is
transported down temperature gradients by heat flow as well as being
transported down pressure gradients by bulk plasma flow. This Nernst advection
causes expulsion of the magnetic field from a hot plasma without a
corresponding change in the plasma density profile, a result which cannot be
explained by common models using purely ideal or resistive
magnetohydrodynamics (MHD).

In general, Nernst advection is the dominant means of magnetic field transport
wherever the speed of the heat flow is faster than both the bulk motion and
the rate of magnetic dissipation, and any models of magnetised plasmas which
neglect the Nernst effect will fail during fast heating processes Willingale
_et al._ (2010); Li  _et al._ (2013). Furthermore, because heat flow depends
on higher order moments of the velocity distribution, a Maxwellian
approximation for heat flow is less accurate than for plasma density or
current. As temperature gradients become steeper, MHD models for Nernst
advection will fail. Under these non-local conditions, when the electron mean
free path is no longer small compared to the length scale of the temperature
gradient, neither the heat flow nor the Nernst velocity are proportional to
the local electron temperature gradient. While the effect of non-locality and
magnetic fields upon the temperature profile has been explored in experiments
Gregori  _et al._ (2004); Froula  _et al._ (2007); Henchen  _et al._ (2018),
non-local changes to the magnetic field have so far only been explored in
kinetic simulations using Vlasov-Fokker-Planck (VFP) codes, which include the
Nernst effect implicitly Ridgers  _et al._ (2008); Joglekar  _et al._ (2016).
Nernst advection therefore make an excellent laboratory to measure kinetic
effects, where changes to the heat dynamics will directly affect the magnetic
field.

We describe a laser-plasma experiment to measure the effect of heatflow on an
applied magnetic field. We focussed a $1.5\,\mathrm{ns}$ duration heater beam
through a nitrogen gas target, propagating anti-parallel to the
$3\,\mathrm{T}$ applied field as shown in Fig. 1. Laser intensities of
$10^{16}\,\mathrm{Wcm^{-2}}$ were reached in a spot size of $19\,\mathrm{\mu
m}$ FWHM over a Rayleigh length of $\approx 1\,\mathrm{mm}$. This produced an
approximately cylindrically-symmetric plasma with electron densities of
$10^{18}-10^{19}\,\mathrm{cm^{-3}}$ and estimated temperatures of around
$1\,\mathrm{keV}$, with a ratio between the cyclotron frequency $\omega_{c}$
and the collision frequency $1/\tau_{e}$ described by a Hall parameter around
$\omega_{c}\tau_{e}\approx 1-10$. Under these conditions, the magnetic field
and heat flow are strongly coupled, with the magnetic field restricting
perpendicular heat flow, but heat flow also affecting the dynamics of the
magnetic field. The cylindrically-symmetric geometry is chosen such that
Biermann and Righi-Leduc Walsh  _et al._ (2020) contributions to changes in
the magnetic field are negligible.

Figure 1: Experimental layout with the Helmholtz coil assembly of the pulsed-
power magnet cut away on one side to show the interaction point. The
$1.5\,\mathrm{ns}$-duration heater beam (solid red) is focussed along the
$z$-axis to a point $2\,\mathrm{mm}$ above the gas jet nozzle. A
$1\,\mathrm{ps}$-duration proton radiography beam (solid red) is focussed onto
a gold foil, producing a proton beam (translucent grey) which passes through
the interaction point along the $x$-axis, perpendicular to the heater beam.
The $1\,\mathrm{ps}$-duration collimated optical probe beam (translucent red)
also passes through the interaction point perpendicular to the heater beam.

The plasma density was measured using optical interferometry assuming
cylindrical symmetry. The interferograms (examples shown in Fig. 2a.i) measure
a plasma column much longer than it is wide, with a fairly uniform diameter.
The resulting density map and radial density profiles are shown in Fig. 2a.ii-
iii for two laser shots conducted under the same conditions, measured at early
and late times ($0.4\,\mathrm{ns}$ and $1.1\,\mathrm{ns}$). The recovered
density demonstrates that $0.4\,\mathrm{ns}$ after the start of the heater
beam, a plasma column has been formed with a diameter of around
$300\,\mathrm{\mu m}$ over a length of slightly under $2\,\mathrm{mm}$
longitudinally, with a peak density around $10^{19}\,\mathrm{cm^{-3}}$. At
these relatively early times, the plasma is not yet fully ionized and the
plasma column shows no sign of cavitation. As the heater beam continues to
ionize more gas and the plasma expands, however, a density cavity forms inside
the plasma column by $1.1\,\mathrm{ns}$ after the start of the heater beam.
The plasma column at this late time is around $800\,\mathrm{\mu m}$ in
diameter.

The proton intensity distribution measured by radiographs, as shown in Fig.
2b.i, can be used to reconstruct the magnetic fields through which the protons
have passed Kugland  _et al._ (2012); Kasim  _et al._ (2019). Because the
proton beam in this experiment was deflected by both the constant applied
magnetic field surrounding the plasma and a smaller signal region within the
plasma itself, we used a deconvolution algorithm to remove the effect of the
background field, accounting for the finite energy absorption range of the
radiochromic film (RCF) and removing blurring (see Methods). The recovered
change in the magnetic fields, is shown in Fig. 2b.ii-iii, where these fields
and the plasma density were measured simultaneously.

Shortly after the start of the heater beam, at $0.4\,\mathrm{ns}$, a strong
reduction in the magnetic field strength by $-2\,\mathrm{T}$ in the central
region is already visible, despite no cavitation in the plasma density. The
applied magnetic field is advected to the edge of the plasma by heat flow,
resulting in an increase in the magnetic field strength further off-axis, at a
radius of around $350\,\mathrm{\mu m}$. The spatial size of the cavitation is
fairly uniform over a length of around $2\,\mathrm{mm}$, with the field
cavitated over the whole of the hot plasma. This decoupling of the magnetic
field profile from the plasma flow is a clear signature of the Nernst effect;
this is the first time this has been measured in experiment.

Figure 2: a) Interferometry results measured $0.4\,\mathrm{ns}$ after the
start of the heater beam (top panels) and $1.1\,\mathrm{ns}$ after (bottom).
(i) The raw interferogram measured on the camera is shown on the left, with
fringe shifts showing the presence of a long plasma column. (ii) From this
interferogram we reconstruct a map of the plasma density, shown as a cross-
section through the centre of the column. (iii) The longitudinally averaged
mean of the radial plasma density profile is shown to the right of this, with
the shaded region showing the standard deviation longitudinally. b)
Radiography results measured at the same times. (i) The raw radiograph is
shown on the left, with darker regions showing a higher proton dose. The areas
of low dose at the left and right edges of the radiograph show the shadow of
the magnet, while the lighter region at the bottom of the radiograph shows the
shadow of the gas cell nozzle. (ii) The change in the magnetic field
reconstructed from the radiograph is shown as a cross-section through the
centre of the plasma column, with (iii) the longitudinally averaged mean and
standard deviation of the radial magnetic field profile to the right.

The magnetic field and density profiles at these two different times are
overlaid in Fig. 3a for comparison. The magnetic field is advected to the
sheath plasma region and within the hot plasma is reduced to less than a third
of its original strength. Magnetic cavitation can be driven by both bulk
plasma flow down pressure gradients (frozen-in-flow) and heat flow down
temperature gradients (Nernst advection), but Fig. 3a shows that Nernst
advection is significantly faster under these conditions. Heat flow drives
cavitation in the magnetic field over a large region, before any cavitation
occurs in the plasma density, with pre-heating reaching out to
$r>0.5\,\mathrm{mm}$. We can therefore estimate the Nernst velocity at
$0.4\,\mathrm{ns}$ by comparing the magnetic field profiles reconstructed from
five different proton radiographs taken on the same shot, each measuring
protons of a different energy. Comparing the times at which the protons pass
through the interaction point with the radius of the peak magnetic field gives
an estimate for the Nernst velocity at these early times of $(6\pm 2)\times
10^{5}\,\mathrm{m/s}$.

The Nernst velocity gives an estimate for the heat flux as
$\phi_{q}=5n_{e}T_{e}v_{N}/2$, which can be compared to the free-streaming
heat flux $\phi_{\mathrm{fs}}=n_{e}T_{e}v_{\mathrm{th},e}$ for a thermal
velocity $v_{\mathrm{th},e}$. Given that the electron thermal velocity at
$1\,\mathrm{keV}$ is $1.9\times 10^{7}\,\mathrm{m/s}$, we can estimate the
heat flux at $0.4\,\mathrm{ns}$ as reaching around one tenth of the free-
streaming limit, showing the importance of correctly modelling the heat
transport at these early times. However, the Nernst velocity falls as time
goes on and the heat flow reduces, with the change in peak magnetic field
position between $0.4\,\mathrm{ns}$ and $1.1\,\mathrm{ns}$ corresponding to an
average advection velocity of just $(2.7\pm 1.0)\times 10^{5}\,\mathrm{m/s}$.
We estimate the average bulk velocity from the half-width at half-maximum of
the density profile at $1.1\,\mathrm{ns}$ as $\approx 3\times
10^{5}\,\mathrm{m/s}$, which is equal to the ion sound speed at a temperature
of around $1\,\mathrm{keV}$. Whereas at early times magnetic field advection
is dominated by hot electrons through the Nernst effect, at later times
hydrodynamic motion on the timescale of ion motion becomes more important.

Figure 3: (a) The reconstructed profiles of the magnetic field (blue) and
density (red) against radius, measured at $0.4\,\mathrm{ns}$ (left panels) and
$1.1\,\mathrm{ns}$ (right) and normalised to a background magnetic field
$B_{0}=3\,\mathrm{T}$ and a fully-ionized density $n_{e0}=2.4\times
10^{19}\,\mathrm{cm^{-3}}$. For comparison, both profiles are longitudinally
averaged over the central $1\,\mathrm{mm}$ of plasma. (b) The magnetic field
profile predicted from one-dimensional simulations, showing an ideal MHD model
without the Nernst effect (dotted line), an extended MHD model including the
thermo-electric Nernst term (dashed black), and results from kinetic VFP
simulations, with Nernst advection included implicitly (solid purple).

We model the plasma and magnetic field evolution with CTC Bissell  _et al._
(2010)– an extended MHD code which includes Nernst advection with a flux-
limited model of heat flow – and a kinetic VFP code, IMPACT Kingham and Bell
(2004), in a 1D planar geometry, to see the effects of the Nernst term and of
different treatments of heat transport. Fig. 3b shows the predictions from
IMPACT and the predictions from CTC both with and without the Nernst term,
with a flux-limiter of $\phi_{q}\leq 0.15\phi_{\mathrm{fs}}$. The scale of
magnetic cavitation cannot be explained without invoking the Nernst effect, as
ideal MHD simulations with the Nernst term turned off predict only slight and
slow-moving cavitation which approximately matches the density profile. Once
the Nernst effect is included, however, the fluid and kinetic simulations
closely agree and both capture the shape of the magnetic field profile at
later times.

On the other hand, neither simulation predicts the long tail in the magnetic
field peak at $0.4\,\mathrm{ns}$ and the rate of advection at early times
observed in the experiment is significantly faster than predicted in either
simulation, which give estimates for the Nernst velocity below around $2\times
10^{5}\,\mathrm{m/s}$. This implies that the plasma was heated by additional
processes beyond inverse bremsstrahlung over a much larger area than the
initial laser spot, with heat already reaching out to radii greater than
$0.5\,\mathrm{mm}$ at $0.4\,\mathrm{ns}$ after the start of the laser pulse.
This could be caused by collective laser-plasma interactions or by significant
wings in the laser profile, as we measured only $25\%$ of the laser power fell
within the central spot at low power, but this is an open question.

That the fluid and kinetic simulations agree so closely is surprising, as the
simulations predict temperatures above $1\,\mathrm{keV}$, giving mean free
paths on the order of 100 microns such that the fluid model should break down.
In the one-dimensional simulations shown here, however, the low collision rate
and the increase in the magnetic field at the edge of the hot plasma – where
the heat flow is highest – mean the maximum Hall parameter reaches
$\omega_{c}\tau_{e}\approx 10$ by $1.1\,\mathrm{ns}$. This both restricts the
heat flow and also keeps the heat flow in the local regime. At early times the
kinetic and fluid simulations predict slightly different heat flows, but at
later times the Nernst effect increasingly leads to a magnetic transport
barrier which limits the rate of Nernst advection and keeps the edge of the
hot plasma in a relatively local regime, even as the magnetic field inside the
cavity falls to zero.

To further explore this effect, laser shots were taken at three different gas
jet backing pressures. The resulting magnetic field profiles are shown in Fig.
4a, measured $1.1\,\mathrm{ns}$ after the start of the heater beam. At lower
densities the plasma is less collisional as
$\tau_{e}\tilde{\propto}T_{e}^{1.5}/n_{e}$, with the electron mean free path
predicted by simulations increasing from $80\,\mathrm{\mu m}$ at
$10.7\,\mathrm{bar}$ backing pressure to $300\,\mathrm{\mu m}$ at
$1\,\mathrm{bar}$. Similarly, the maximum Hall parameter predicted by
simulations increases to $\omega_{c}\tau_{e}\approx 40$ at the lowest plasma
density. The rate of inverse bremsstrahlung heating is proportional to the
collision frequency and so at the lower backing pressures the plasma is also
colder. This means both that the speed of heat flow is lower at lower
densities – leading to slower magnetic advection and less cavitation as
observed in the experiment – and also that the magnetic barrier further
constrains the heat flow and keeps the edge of the plasma in the relatively
local regime, despite the long mean free paths.

We estimate how the Nernst advection rates change with density by measuring
the position of the peak in the magnetic field at $1.1\,\mathrm{ns}$ in both
the experiment and 1D simulations; these results are shown in Fig. 4b. In all
cases, the advection velocity falls with decreasing density as expected, with
the simulations largely reproducing the trend measured in experiment despite
predicting significantly lower advection velocities. Fitting the measured
average advection velocities to a power law gives a trend $v_{N}\propto
n_{e0}^{0.30\pm 0.03}$, which reflects the dependence of the heating rates on
the plasma density. Although the Hall parameter is around a factor of four
higher at the lowest density, the advection velocity is only reduced by a
factor of two. We are therefore studying an interesting mixed regime, where
the magnetic field strongly suppresses the heat flow and keeps the plasma in a
relatively local regime, but the Nernst advection is still faster than would
be expected for a strongly magnetised plasma, particularly at early times
before the magnetic barrier grows large.

Comparing the local and kinetic models, at the higher density of $2.4\times
10^{19}\,\mathrm{cm^{-3}}$, the extended MHD and VFP simulations predict the
same Nernst velocities over time and the same position for the peak in the
magnetic field, with an average advection velocity up to $1.1\,\mathrm{ns}$ of
$3.3\times 10^{5}\,\mathrm{m/s}$ and $3.2\times 10^{5}\,\mathrm{m/s}$ for the
VFP and MHD simulations respectively. At the lowest density, however, the
predictions begin to diverge, with the MHD simulation predicting an average
advection velocity around $10\%$ larger than predicted by the VFP simulation
at $2.2\times 10^{18}\,\mathrm{cm^{-3}}$; here a flux-limiter of 0.05 gives
much closer agreement. Because of the magnetisation of the plasma, fluid
models are a good approximation, but to precisely match fluid simulations to
kinetic simulations still requires tuning the flux-limiter to the plasma
conditions.

Figure 4: a) The recovered magnetic field profiles measured $1.1\,\mathrm{ns}$
after the arrival of the heater beam for three different backing pressures,
showing the mean and standard deviation of the magnetic field over a
$1\,\mathrm{mm}$ long section in the middle of the gas jet. b) Comparing
results from the simulations and the experiments, the average advection
velocity of the magnetic field in the time up to $1.1\,\mathrm{ns}$ is
estimated by the position of the peak in the magnetic field.

In summary, we have measured the change in an applied magnetic field when an
underdense plasma is heated by a ns-duration laser pulse. In doing so, we have
made the first direct measurement of magnetic cavitation driven by heat flow
rather than by bulk motion in the plasma. This magnetic cavitation is
particularly relevant for experiments into magnetic reconnection – where rapid
heating means that magnetic transport is often Nernst-dominated – and for
inertial confinement fusion experiments, where applied or self-generated
magnetic fields have been shown to increase temperatures in the hot-spot and
mitigate instability growth Froula  _et al._ (2007); Chang  _et al._ (2011);
Walsh  _et al._ (2019). As described in refs. Slutz  _et al._ (2010); McBride
and Slutz (2015), the expulsion of magnetic fields from the hottest regions of
the plasma will bring into question the viability of magnetised inertial
confinement fusion techniques. We have shown that models without the Nernst
term result in a spuriously high magnetic field within the plasma, and that in
this regime extended MHD models agree surprisingly well with kinetic
simulations, with the heat flow at the edge of the hot plasma remaining
relatively local due to the increase in the magnetic field outside the hot
plasma.

###### Acknowledgements.

The authors are grateful for the support of LLNL Academic Partnerships
(B618488), EUROfusion Enabling Research Grants AWP17-ENR-IFE-CCFE-01 and
AWP17-ENR-IFE-CEA-02, and UK EPSRC grants EP/P026796/1, EP/R029148/1,
EP/M01102X/1 and EP/M011372/1. The authors particularly wish to thank the
staff at Vulcan and Target Fabrication at the Central Laser Facility for all
their support. Radiography calibration data from David Carroll and James Green
were indispensable and we are grateful for advice with CTC from John Bissell.
Part of this project was undertaken on the Viking Cluster, which is a high
performance compute facility provided by the University of York. We are
grateful for computational support from the University of York High
Performance Computing service, Viking and the Research Computing team. The
experiment was designed by NW, CPR, and MPR and planned by CA, PB, GSH, OCE,
LA, ZN, and NW. GSH and PB were the target area operators, and MN was the
facility link scientist. CA led the proton radiography set-up, SA and GSH were
responsible for the pulsed power magnet, OCE designed and built the optical
probe layout, and KG built the system used for timing. PB, LA and MK worked on
all aspects of the experiment. AD and CAW conducted fluid simulations, and CA
and CPR conducted VFP simulations with a code originally written by RJK. CA
conducted the radiography and interferometry analysis with PB, and led the
composition of the manuscript, with contributions and revisions from PB, GSH,
OCE, RJK, ZN, CPR and NW.

## References

  * Biermann (1950) L. Biermann, Zeitschrift Naturforschung Teil A 5, 65 (1950).
  * Braginskii (1958) S. I. Braginskii, Journal of Experimental and Theoretical Physics 6, 358 (1958).
  * Haines (1986) M. G. Haines, Plasma Phys. Control. Fusion 28, 1705 (1986).
  * Borghesi  _et al._ (2006) M. Borghesi, J. Fuchs, S. V. Bulanov, A. J. MacKinnon, P. K. Patel, and M. Roth, Fusion Science and Technology 49, 412 (2006).
  * Sefkow  _et al._ (2014) A. B. Sefkow, S. A. Slutz, J. M. Koning, M. M. Marinak, K. J. Peterson, D. B. Sinars, and R. A. Vesey, Physics of Plasmas 21, 072711 (2014).
  * Behnia and Aubin (2016) K. Behnia and H. Aubin, Rep. Prog. Phys. 79, 046502 (2016).
  * Nishiguchi  _et al._ (1984) A. Nishiguchi, T. Yabe, M. G. Haines, M. Psimopoulos, and H. Takewaki, Phys. Rev. Lett. 53, 262 (1984).
  * Willingale  _et al._ (2010) L. Willingale, A. G. R. Thomas, P. M. Nilson, M. C. Kaluza, S. Bandyopadhyay, A. E. Dangor, R. G. Evans, P. Fernandes, M. G. Haines, C. Kamperidis, R. J. Kingham, S. Minardi, M. Notley, C. P. Ridgers, W. Rozmus, M. Sherlock, M. Tatarakis, M. S. Wei, Z. Najmudin, and K. Krushelnick, Phys. Rev. Lett. 105, 095001 (2010).
  * Li  _et al._ (2013) C. Li, F. Séguin, J. Frenje, N. Sinenian, M. Rosenberg, M.-E. Manuel, H. Rinderknecht, A. Zylstra, R. Petrasso, P. Amendt, O. Landen, A. Mackinnon, R. Town, S. Wilks, R. Betti, D. Meyerhofer, J. Soures, J. Hund, J. Kilkenny, and A. Nikroo, Nucl. Fusion 53, 073022 (2013).
  * Gregori  _et al._ (2004) G. Gregori, S. H. Glenzer, J. Knight, C. Niemann, D. Price, D. H. Froula, M. J. Edwards, R. P. J. Town, A. Brantov, W. Rozmus, and V. Y. Bychenkov, Phys. Rev. Lett. 92, 205006 (2004).
  * Froula  _et al._ (2007) D. Froula, J. Ross, B. Pollock, P. Davis, A. James, L. Divol, M. Edwards, A. Offenberger, D. Price, R. Town, G. Tynan, and S. Glenzer, Phys. Rev. Lett. 98, 135001 (2007).
  * Henchen  _et al._ (2018) R. J. Henchen, M. Sherlock, W. Rozmus, J. Katz, D. Cao, J. P. Palastro, and D. H. Froula, Phys. Rev. Lett. 121, 125001 (2018).
  * Ridgers  _et al._ (2008) C. P. Ridgers, R. J. Kingham, and A. G. R. Thomas, Phys. Rev. Lett. 100, 075003 (2008).
  * Joglekar  _et al._ (2016) A. S. Joglekar, C. P. Ridgers, R. J. Kingham, and A. G. R. Thomas, Phys. Rev. E 93, 043206 (2016).
  * Walsh  _et al._ (2020) C. A. Walsh, J. P. Chittenden, D. W. Hill, and C. Ridgers, Physics of Plasmas 27, 022103 (2020).
  * Kugland  _et al._ (2012) N. L. Kugland, D. D. Ryutov, C. Plechaty, J. S. Ross, and H.-S. Park, Review of Scientific Instruments 83, 101301 (2012).
  * Kasim  _et al._ (2019) M. F. Kasim, A. F. A. Bott, P. Tzeferacos, D. Q. Lamb, G. Gregori, and S. M. Vinko, Phys. Rev. E 100, 033208 (2019).
  * Bissell  _et al._ (2010) J. J. Bissell, C. P. Ridgers, and R. J. Kingham, Phys. Rev. Lett. 105, 175001 (2010).
  * Kingham and Bell (2004) R. J. Kingham and A. R. Bell, Journal of Computational Physics 194, 1 (2004).
  * Chang  _et al._ (2011) P. Y. Chang, G. Fiksel, M. Hohenberger, J. P. Knauer, R. Betti, F. J. Marshall, D. D. Meyerhofer, F. H. Séguin, and R. D. Petrasso, Phys. Rev. Lett. 107, 035006 (2011).
  * Walsh  _et al._ (2019) C. A. Walsh, K. McGlinchey, J. K. Tong, B. D. Appelbe, A. Crilly, M. F. Zhang, and J. P. Chittenden, Physics of Plasmas 26, 022701 (2019).
  * Slutz  _et al._ (2010) S. A. Slutz, M. C. Herrmann, R. A. Vesey, A. B. Sefkow, D. B. Sinars, D. C. Rovang, K. J. Peterson, and M. E. Cuneo, Physics of Plasmas 17, 056303 (2010).
  * McBride and Slutz (2015) R. D. McBride and S. A. Slutz, Physics of Plasmas 22, 052708 (2015).


# Satellite Internet of Things Research Report

Zhang Shutao

##  1 Research Overview

This section introduces satellite IoT from three perspectives: background
introduction, demand analysis, and the development status at home and abroad
[1, 2, 3, 4, 5, 6].

###  1.1 Background Introduction

Satellite communication is a method of communication between two or more earth
stations using artificial earth satellites as relay stations. It has
advantages such as wide coverage, large communication capacity, good
durability, and strong adaptability, making it an important means to achieve
seamless global communication. The world’s first artificial satellite was
launched by the Soviet Union in October 1957, which sent signals back to
Earth. The first synchronous communication satellite was launched by NASA in
July 1963, but it was not yet a geostationary satellite. The initial semi-
experimental, semi-practical geostationary satellite ”Early Bird” was launched
in April 1965 for commercial satellite communication between Europe and
America, marking the practical stage of satellite communication.

Satellite communication systems include all equipment for communication and
ensuring communication, generally consisting of four parts: space subsystem,
communication earth station, tracking telemetry command subsystem, and
monitoring management subsystem, as shown in Figure 1. The main body of the
space subsystem is the communication satellite, which mainly includes one or
more transponders, each capable of simultaneously receiving and retransmitting
signals from multiple earth stations, thus serving as a relay station. The
communication earth station is a microwave radio transmission and reception
station, through which users access satellite lines for communication. The
tracking telemetry command subsystem is responsible for tracking and measuring
the satellite to ensure it accurately enters the designated position in the
geostationary orbit. After the satellite is in normal operation, it needs to
periodically correct its orbital position and maintain its attitude. The
monitoring management subsystem is responsible for detecting and controlling
the communication performance of the fixed satellite before and after the
service is activated, such as monitoring the basic communication parameters
like satellite transponder power, satellite antenna gain, RF frequency, and
bandwidth to ensure normal communication.

Currently, the frequency bands used by satellites mainly include C-band, Ku-
band, and Ka-band. According to type, satellites can be divided into
scientific satellites, experimental satellites, and application satellites.
According to application, satellites can be classified into communication
satellites, meteorological satellites, reconnaissance satellites, navigation
satellites, and astronomical satellites. Based on orbit altitude, satellites
can be classified into the following three categories:

Figure 1: Basic Composition of Satellite Communication System

  * •

Low Earth Orbit (LEO) Satellites: Orbit altitude between 700 and 1500 km, with
an orbital period of 2 to 4 hours. LEO satellites have advantages such as
reduced propagation delay and lower transmission loss. A constellation of
multiple LEO satellites can achieve seamless global coverage.

  * •

Middle Earth Orbit (MEO) Satellites: Orbit altitude between 8000 and 20000 km,
with an orbital period of 4 to 12 hours.

  * •

High Earth Orbit (HEO) Satellites: Orbit altitude greater than 20000 km,
including geostationary satellites at about 35786 km, with an orbital period
of one sidereal day, i.e., 23 hours, 56 minutes, and 4 seconds. When the
orbital inclination of the geostationary satellite relative to the equatorial
plane is zero, it is called a geostationary orbit (GEO).

Since its first proposal at MIT in 1999, the IoT has received significant
attention. Traditional IoT can be divided into three layers: the perception
layer, the network layer, and the application layer, transmitted through local
area network methods such as WIFI, Bluetooth, and Zigbee. With the widespread
application and continuous maturation of IoT technology, Low Power Wide Area
Network (LPWAN) has been proposed, including technologies like Extended
Coverage-GSM (EC-GSM) operating in licensed bands, Narrowband IoT (NB-IoT),
and LoRa, Sigfox in unlicensed bands, aiming to provide services for IoT
applications requiring long-distance transmission, low power consumption, and
massive connectivity. The 3GPP has stated that NB-IoT will continue to evolve
to support massive Machine Type Communications (mMTC) scenarios in 5G, aiding
the development of 5G IoT.

The International Telecommunication Union (ITU) proposed four application
scenarios for satellite and 5G integration: cell backhaul, relay to station,
communication on the move, and hybrid multicast. The 3rd Generation
Partnership Project (3GPP) has proposed corresponding protocols for the
satellite-ground integration architecture in Release 15 (R15), Release 16
(R16), and Release 17 (R17) [7, 8, 9]. The SaT5G Alliance focuses on
researching communication technologies for satellite and 5G integration and
demonstrated its validation platform at the European Conference on Networks
and Communications in 2018.

###  1.2 Demand Analysis

Traditional IoT already supports a variety of applications, such as smart
agriculture, smart home, and smart transportation. However, due to the diverse
terrain on Earth, the construction of base stations for ground communication
networks is limited by natural environments and geographical locations, making
it difficult to cover areas like deserts, forests, and oceans. Satellite
communication networks can complement ground communication networks in terms
of coverage. Satellites are distributed in the sky and are not limited by
geographical locations. A well-designed satellite constellation can provide
all-weather, seamless global coverage and, compared to ground communication
networks, offers higher reliability and resilience in cases of earthquakes,
floods, and other disasters.

Therefore, the so-called satellite IoT is the IoT that uses satellite
communication networks for information transmission. Satellite IoT can achieve
wide-area coverage, long-distance transmission, and information collection in
remote areas, playing a crucial role in fields such as field exploration,
marine environment monitoring, and global emergency search and rescue. In
2015, Liu Gang and others proposed the space-based IoT, and with continuous
research, the architecture and construction ideas of the space-based IoT have
been proposed.

###  1.3 Development Status at Home and Abroad

Although the application of satellite communication in IoT has not yet been
explicitly proposed domestically or internationally, many systems fall under
the category of satellite IoT. Examples include foreign systems like Orbcomm,
Argo, Iridium, Globalstar, and domestic systems like Beidou, Hongyan, and
Xingyun.

The Orbcomm satellite system, built by Orbital Sciences Corporation of the USA
and Teleglobe of Canada, started commercial operation in November 1998. It
includes 36 satellites, each weighing 43 kg. Users can collect remote data,
monitor vehicle locations, and send and receive short messages through this
system. The Argo satellite system, established by the French National Centre
for Space Studies, NASA, and the National Oceanic and Atmospheric
Administration, has an orbital altitude of 850 km and is mainly used for real-
time global ocean monitoring. The Iridium satellite system, launched by
Iridium Communications, consists of 66 satellites, each weighing around 670
kg, providing burst data services globally, mainly for the US military. The
Globalstar satellite system, initiated by Loral Corporation and Qualcomm,
includes 48 low-orbit satellites with an orbital altitude of about 1414 km,
offering seamless satellite mobile communication services to users.
Additionally, some satellite IoT systems are under construction, such as
HeliosWire of Canada, planning to launch 30 satellites to support data
collection from 5 billion sensors, and Fleet Space Technologies of Australia,
aiming to build a nano-satellite constellation to help global IoT devices
achieve low-bandwidth connections, with the first batch of 1 million terminals
already booked. In China, the third-generation Beidou Navigation Satellite
System has significant applications in fields like transportation, marine
fisheries, and emergency rescue. The remote monitoring system for power
transmission facilities in the Yulin Substation of Guangxi is a pilot
application based on the Beidou Navigation Satellite System, effectively
saving manpower, improving efficiency, and reducing costs. The Hongyan
Satellite System, under construction by China Aerospace Science and Technology
Corporation, plans to collect data information through a constellation of 60
low-orbit small satellites, achieving all-weather, all-time, global coverage
for two-way communication. The ”Xingyun Project” by China Aerospace Science
and Industry Corporation aims to build a satellite IoT platform using 80 low-
orbit satellites to provide communication services for global IoT terminals.

##  2 Technical Characteristics and Architecture of Satellite IoT

###  2.1 Technical Characteristics

The technical characteristics of satellite IoT are mainly reflected in the
following aspects:

  * •

Wide Coverage and Large Capacity: The use of satellite communication can
overcome the limitations of ground networks, providing global coverage,
especially in remote, mountainous, and ocean areas where ground communication
infrastructure is lacking.

  * •

High Reliability and Strong Disaster Resistance: Satellite communication is
less affected by natural disasters and can maintain communication even in
extreme conditions such as earthquakes, floods, and fires.

  * •

Flexible Networking and Rapid Deployment: Satellite IoT can provide flexible
networking options and be quickly deployed without being constrained by ground
infrastructure construction.

  * •

Low Power Consumption and Long Battery Life: IoT devices in satellite IoT
systems can achieve low power consumption and long battery life through
optimized design and efficient communication protocols.

  * •

Secure and Private Communication: Satellite IoT can provide secure and private
communication services through encryption and authentication mechanisms,
ensuring data security and user privacy.

###  2.2 Architecture of Satellite IoT

The architecture of satellite IoT mainly includes three layers: the space
layer, the ground layer, and the user layer, as shown in Figure 2.

Figure 2: Architecture of Satellite IoT

  * •

Space Layer: The space layer mainly consists of low earth orbit (LEO)
satellites, medium earth orbit (MEO) satellites, and geostationary earth orbit
(GEO) satellites. These satellites form a constellation to provide global
coverage and communication services.

  * •

Ground Layer: The ground layer mainly consists of gateway stations, monitoring
and control centers, and network management centers. The gateway stations are
responsible for the communication between the space layer and the ground
layer, converting satellite signals into terrestrial network signals. The
monitoring and control centers are responsible for the operation, monitoring,
and control of the satellites, ensuring the normal operation of the satellite
constellation. The network management centers are responsible for the
management of the entire satellite IoT network, including resource allocation,
performance monitoring, and fault management.

  * •

User Layer: The user layer mainly consists of various IoT terminals and user
equipment. IoT terminals include sensors, actuators, and communication
modules, which collect and transmit data. User equipment includes mobile
phones, computers, and other devices that access the satellite IoT network
through the gateway stations.

Figure 3: The integrated architecture of satellite communication and 5G system
[10, 11, 12].

##  3 Key Technologies of Satellite IoT

###  3.1 Satellite Communication Technology

Satellite communication technology is the foundation of satellite IoT, mainly
including satellite communication systems, satellite transponders, satellite
antennas, and satellite communication protocols.

  * •

Satellite Communication Systems: Satellite communication systems include space
subsystems, ground stations, and user terminals. The space subsystem consists
of communication satellites and their payloads, which receive, amplify, and
retransmit signals. The ground stations are responsible for the uplink and
downlink of signals, converting satellite signals into terrestrial network
signals. The user terminals are devices that communicate with the satellites,
such as IoT terminals and user equipment.

  * •

Satellite Transponders: Satellite transponders are devices that receive,
amplify, and retransmit signals in the satellite communication system. They
are the core components of communication satellites, determining the
communication capacity and coverage of the satellite.

  * •

Satellite Antennas: Satellite antennas are devices that transmit and receive
signals between the satellites and the ground stations. They include reflector
antennas, phased array antennas, and microstrip antennas, among others.

  * •

Satellite Communication Protocols: Satellite communication protocols are the
rules and standards for communication between satellites, ground stations, and
user terminals. They include frequency allocation, modulation and coding
schemes, and communication procedures.

###  3.2 IoT Communication Technology

IoT communication technology is the key to realizing the connection and
communication between IoT devices, mainly including short-range communication
technology, long-range communication technology, and low-power wide-area
network (LPWAN) technology.

  * •

Short-Range Communication Technology: Short-range communication technology
includes Wi-Fi, Bluetooth, Zigbee, and other technologies, which are suitable
for short-distance and high-speed data transmission.

  * •

Long-Range Communication Technology: Long-range communication technology
includes cellular communication, satellite communication, and other
technologies, which are suitable for long-distance and large-area data
transmission.

  * •

Low-Power Wide-Area Network (LPWAN) Technology: LPWAN technology includes NB-
IoT, LoRa, Sigfox, and other technologies, which are suitable for long-
distance, low-power, and large-scale IoT applications.

###  3.3 Edge Computing and Cloud Computing Technology

Edge computing and cloud computing technology are important support
technologies for satellite IoT, mainly including data processing, storage, and
analysis.

  * •

Edge Computing: Edge computing refers to the processing and analysis of data
at the edge of the network, close to the source of the data. It can reduce the
latency and bandwidth consumption of data transmission, improve the real-time
performance and efficiency of data processing, and enhance the security and
privacy of data.

  * •

Cloud Computing: Cloud computing refers to the processing and analysis of data
in the cloud, providing scalable, flexible, and cost-effective computing and
storage resources. It can support large-scale data processing and analysis,
enable remote access and collaboration, and provide advanced analytics and
machine learning capabilities.

###  3.4 Study on Low Latency Network Slicing Technology for IoT

Figure 4: SDN and NFV framework for network slicing.

  * •

In order to provide a low-latency network environment for the deployment of
edge computing nodes and handover scenarios, it is necessary to design an
efficient 5G network slicing strategy. Research Topic 2 aims to address the
issue of building a 5G network slicing topology by dividing network slices
from the control plane and user plane based on SDN (Software-Defined
Networking) and NFV (Network Functions Virtualization). On this basis, it will
manage and orchestrate network slice resources, dynamically adjust path
weights using backpropagation neural network theory, and determine the optimal
mapping path using heuristic algorithms to resolve latency issues in 5G
network slicing.

  * •

2.2.1 Research on Network Slicing Architecture Based on SDN and NFV Technology
The proposed method draws on the SDN concept of separating data and control
planes, dividing network slices from both the control plane and the user plane
to facilitate the orchestration and management of user plane network slices by
the control plane network slices. Simultaneously, NFV is used to virtualize
the network functions of the access network and the core network, achieving
software-hardware decoupling, thereby constructing an end-to-end network
slicing architecture.

  * •

Scientific Issue 2: In IoT networks, the emergence of various types of
services makes it crucial to reasonably divide network slices and avoid
congestion. How to design an efficient network slicing strategy, build a
network architecture that can quickly forward data, manage and orchestrate
network slice resources, and find the shortest mapping path for network slices
to reduce transmission latency is the second problem this project aims to
solve. This project intends to use SDN and NFV technologies to segment and
virtualize the network functions of the access network, transport network, and
core network, rapidly processing network slices from the user plane and data
plane to meet the service demands of different applications. It will also
manage and orchestrate network slice resources, using a backpropagation neural
network approach to train with large amounts of sample data and dynamically
adjust path weights. On this basis, heuristic algorithms will be used to
traverse and find the optimal mapping path for network slices, thus improving
transmission efficiency and providing a suitable network environment for the
deployment of edge computing nodes and handover scenarios.

##  4 Application Scenarios of Satellite IoT

Satellite IoT has a wide range of application scenarios, mainly including
smart agriculture, smart transportation, smart cities, environmental
monitoring, and emergency response.

###  4.1 Smart Agriculture

Satellite IoT can support smart agriculture by providing real-time monitoring
and control of agricultural activities, such as soil moisture, crop growth,
and pest control. It can enable precision agriculture, optimize resource use,
and improve crop yield and quality.

###  4.2 Smart Transportation

Satellite IoT can support smart transportation by providing real-time
monitoring and management of transportation systems, such as vehicle location,
traffic conditions, and road safety. It can enable intelligent transportation
systems, reduce congestion and accidents, and improve transportation
efficiency and safety.

###  4.3 Smart Cities

Satellite IoT can support smart cities by providing real-time monitoring and
management of urban infrastructure and services, such as energy, water, waste,
and public safety. It can enable smart city applications, improve resource
use, and enhance the quality of life for residents.

###  4.4 Environmental Monitoring

Satellite IoT can support environmental monitoring by providing real-time data
on environmental conditions, such as air quality, water quality, and weather.
It can enable early warning systems, support environmental protection, and
enhance disaster response and resilience.

###  4.5 Emergency Response

Satellite IoT can support emergency response by providing real-time
communication and coordination in disaster situations, such as earthquakes,
floods, and fires. It can enable rapid response, improve situational
awareness, and enhance rescue and recovery efforts.

##  5 Conclusion

Satellite IoT is an emerging technology that combines the advantages of
satellite communication and IoT, providing global coverage, high reliability,
and flexible networking. It has a wide range of applications in various
fields, including smart agriculture, smart transportation, smart cities,
environmental monitoring, and emergency response. With the continuous
development of satellite communication, IoT, edge computing, cloud computing,
AI, and ML technology, satellite IoT will play an increasingly important role
in the future, supporting the digital transformation and sustainable
development of society.

## References

  * [1] S. Zhang, S. Zeng, F. Ye, R. Tang, P. Wu, and M. Xia, “An efficient downlink receiver design for NB-IoT,” in _2020 IEEE Wireless Communications and Networking Conference (WCNC)_. IEEE, 2020, pp. 1–6.
  * [2] B. Yu, S. Zhang, X. Dai, and H. Zhang, “Iterative decoder for coded SEFDM systems,” in _2017 IEEE 17th International Conference on Communication Technology (ICCT)_. IEEE, 2017, pp. 145–150.
  * [3] X. Ning, S. Zhang, X. Zheng, and T.-H. Chang, “Multi-grid-based localized statistical channel modeling: A radio map approach,” in _2022 International Symposium on Wireless Communication Systems (ISWCS)_. IEEE, 2022, pp. 1–6.
  * [4] Y. Li, S. Zhang, X. Ren, J. Zhu, J. Huang, P. He, K. Shen, Z. Yao, J. Gong, T. Chang _et al._ , “Real-world wireless network modeling and optimization: From model/data-driven perspective,” _Chinese Journal of Electronics_ , vol. 31, no. 6, pp. 991–1012, 2022.
  * [5] S. Zhang, Y. Xue, Q. Shi, and T. Chang, “Statistical channel modeling methods in wireless network twinning: current status and frontiers,” _ZTE technology journal_ , vol. 29, no. 3, pp. 26–31, 2023.
  * [6] S. Zhang, X. Ning, X. Zheng, Q. Shi, T.-H. Chang, and Z.-Q. Luo, “A physics-based and data-driven approach for localized statistical channel modeling,” _IEEE Transactions on Wireless Communications_ , 2023.
  * [7] 3GPP, TS 38.811: “Study on New Radio (NR) to support non-terrestrial networks (R15)”, 2019.
  * [8] 3GPP, TS 22.822: “Study on using Satellite Access in 5G (R16)”, 2018.
  * [9] 3GPP, TS 22.261: “Service requirements for the 5G system (R17)”, 2019.
  * [10] C. Suzhi, W. Junyong, H. Hao, Z. Yi, Y. Shuling, Y. Lei, W. Shaojun, and G. Yongsheng, “Space edge cloud enabling network slicing for 5G satellite network,” in _Proceedings of International Wireless Communications Mobile Computing Conference (IWCMC)_ , June 2019, pp. 787–792.
  * [11] B. T. Jou, O. Vidal, J. Cahill, F. Arnal, L. Honssin, M. Boutin, and D. K. Chau, “Architecture options for satellite integration into 5G networks,” in _Proceedings of European Conference on Networks and Communications (EuCNC)_ , June 2018, pp. 398–399.
  * [12] L. Boero, R. Bruschi, F. Davoli, M. Marchese, and F. Patrone, “Satellite networking integration in the 5G ecosystem: Research trends and open challenges,” _IEEE Network_ , vol. 32, no. 5, pp. 9–15, Sept. 2018\.