# New insights on divertor parallel flows, ExB drifts, and fluctuations from
in situ, two-dimensional probe measurement in the Tokamak à Configuration
Variable

H. De Oliveira1, C. Theiler1, O. Février1, H. Reimerdes1, B. P. Duval1, C.
Tsui2, S. Gorno1, D. S. Oliveira1, A. Perek3, the TCV Teama 1École
Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015
Lausanne, Switzerland.  2Center for Energy Research (CER), University of
California San Diego (UCSD), La Jolla, California 92093-0417, USA  3Dutch
Institute for Fundamental Energy Research, De Zaale 20, 5612 AJ Eindhoven,
Netherlands.  aSee the author list of H. Reimerdes et al 2022 _Nucl. Fusion_
62 042018\<EMAIL_ADDRESS>
(August 28, 2024)

###### Abstract

In-situ, two-dimensional (2D) Langmuir probe measurements across a large part
of the TCV divertor are reported in L-mode discharges with and without
divertor baffles. This provides detailed insights into time averaged profiles,
particle fluxes, and fluctuation behavior in different divertor regimes. The
presence of the baffles is shown to substantially increase the divertor
neutral pressure for a given upstream density and to facilitate the access to
detachment, an effect that increases with plasma current. The detailed, 2D
probe measurements allow for a divertor particle balance, including ion flux
contributions from parallel flows and $E\times B$ drifts. The poloidal flux
contribution from the latter is often comparable or even larger than the
former, such that the divertor parallel flow direction reverses in some
conditions, pointing away from the target. In most conditions, the integrated
particle flux at the outer target can be predominantly ascribed to ionization
along the outer divertor leg, consistent with a closed-box approximation of
the divertor. The exception is a strongly detached divertor, achieved here
only with baffles, where the total poloidal ion flux even decreases towards
the outer target, indicative of significant plasma recombination. The most
striking observation from relative density fluctuation measurements along the
outer divertor leg is the transition from poloidally uniform fluctuation
levels in attached conditions to fluctuations strongly peaking near the
X-point when approaching detachment.

††:

##  1 Introduction

Particle and heat exhaust in next generation tokamaks such as ITER and DEMO
remains an outstanding issue that must be addressed in order to maintain
plasma facing components in working condition whilst maintaining acceptable
core performance. The transport of energy and particles within the boundary of
tokamaks is governed by a complex interplay of cross-field turbulent transport
and steady-state drifts, strong transport parallel to the magnetic field
together with sources and sinks. With this complexity, extrapolation towards
higher power tokamaks is challenging, requiring detailed experimental insights
and comparison with theory on today’s experiments. TCV, a tokamak [1] at EPFL,
is a graphite wall machine with exceptional magnetic poloidal shaping
capabilities. It can access a wide range of configurations, that may be used
to shed light upon the complex boundary dynamics and assist in model
validation.

Figure 1:  a) Poloidal view of the RDPA diagnostic structure below TCV, b)
RDPA in vessel picture taken during machine opening, c) $D4\rightarrow 2$
light snapshot recorded with the MANTIS camera system [2] during an experiment
and d) Illustration of the magnetic geometry used in this work together with
the baffles, gas valves and the spatial coverage of the most relevant
diagnostics used in this study: Thomson Scattering (TS), RDPA and wall probes.
The blue shaded rectangle represents the region accessed by RDPA during an
up/down reciprocation.

In this work, which is an extension of the work illustrated in Chapters 4 and
6 of Ref. [3], we report on two-dimensional (2D) Langmuir probe measurements
across a large part of TCV’s divertor region, providing a unique experimental
approach to the measurement of divertor particle fluxes.. The measurements are
enabled by a new, fast Reciprocating Divertor Langmuir Probe Array (RDPA) [4].
Specifically, in the divertor geometry studied in this work, RDPA provides 2D
profiles along the outer divertor leg, from the combination of a radial array
of probes and an extended vertical sweep, Figure 1. The quantities obtained
include plasma density, electron temperature, potential, parallel ion Mach
number, and density fluctuation levels. They are used to perform a particle
balance analysis in the TCV divertor for different divertor regimes with and
without TCV’s divertor baffles [5, 6]. The particle balance study reveals that
$E\times B$ drifts often play an important role, as previously observed in
DIII-D [7, 8, 9], and that a closed-box approximation [10, 11] is a relatively
good assumption for the TCV divertor, except for when the plasma is strongly
detached. Another interesting observation is a reversal of the parallel flow
in the downward $E\times B$ region in certain conditions. Regarding divertor
density fluctuations, a key observation is the appearance of a strong poloidal
gradient of the turbulence level at high collisionality, where the fluctuation
near the target become much weaker than near the X-point.

The paper is organized as follows. A description of the experimental setup is
presented in Section 2, followed by the analysis performed to deduce the most
relevant quantities from the RDPA in Section 3. The main experimental results
are presented in Section 4 and Section 5. Finally, a discussion and summary of
the paper is presented in Section 6.

##  2 Experimental setup

Figure 2:  Time traces of relevant plasma properties from the low density
reference $\\#65964$ without baffles and the low density reference $\\#64766$
with baffles: a) plasma current, b) ohmic power (no external heating source
has been used in this study), c) vertical position of the RDPA probe and
X-point height, d) stored energy computed from magnetic measurements, e) line
averaged density from interferometry measurements, f) total radiated power
from bolometry measurements, g) deuterium gas flow and h) divertor neutral
pressure from baratron measurements.

The present divertor particle balance studies are performed in Lower Single
Null (LSN) Ohmic L-mode configurations with a toroidal magnetic field
$B_{t}\approx 1.4\leavevmode\nobreak\ \mathrm{T}$ and constant plasma current
$I_{p}\approx 320\leavevmode\nobreak\ \mathrm{kA}$, Figure 1d). The toroidal
field is in the so-called ’reversed’ direction, corresponding to an upward ion
$\vec{B}\times{\nabla\vec{B}}$ drift that is unfavorable to H-mode access.
$I_{p}=320\leavevmode\nobreak\ \mathrm{kA}$ is chosen, resulting in a $q_{95}$
of $\approx 2.4$. This choice results in magnetic field lines with relatively
large pitch angle, limiting the total fraction of field lines that are
intercepted by the RDPA horizontal probe arm in the divertor outer leg to less
than 15%. A high plasma current also permits a higher line averaged density.
In these experiments, the line averaged core density $\left<n_{e}\right>$was
varied from $5\times 10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$ up to
$13\times 10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$ to access both attached
and detached divertor conditions.

Edge physics experiments are often conducted with density ramps in TCV [12] to
study the plasma evolution from attached to detached within the same
discharge. Since RDPA vertical plunges last typically $\approx
0.35\leavevmode\nobreak\ \mathrm{s}$ (limited by the motor power), the
measurements during a density ramp would not provide 2D divertor profiles with
consistent conditions. Therefore, multiple discharges were performed with
constant core densities. The RDPA was found to have a negligible effect on the
relevant main plasma properties such as radiated power, stored energy, line
averaged density, Ohmic power, gas fueling and divertor pressure. These
quantities remain constant across the reciprocation period, as shown in Figure
2. RDPA produces, however, a characteristic shadow downstream, with a plasma
density lower than in the surrounding and data from the floor LPs influenced
by this shadow were discarded.

Figure 3:  a) and e) Magnetic equilibrium reconstruction and relevant Langmuir
probe coverage highlighted on the walls, b) and f) Integrated outer target ion
flux as a function of $\langle n_{e}\rangle$, c) and g) CIII front altitude
obtained from the multi spectral imaging MANTIS system [2] and d) and e)
divertor neutral pressure obtained from the baratron gauge. Shots without
baffles are shown in a), b), c) and d): constant density experiments #65964,
#66210, #66220 and #66222 represented with triangles and the density ramp
#66208 represented with scattered points. Shots with baffles are shown in e),
f), g) and h): constant density experiments #64766, #63963, #64965 and #64962
represented with triangles and the density ramp #64900 with scattered points.
CIII data for the shot #64766 could not be acquired.

The total integrated ion flux density at the outer target, the CIII emission
front position (a proxy for low electron temperature conditions) along the
outer leg [12] and the divertor neutral pressure, all given as a function of
the line averaged density, are found similar with density ramps and with
constant density, as shown in Figure 3. This indicates that the divertor
conditions, specifically including neutral dynamics and impurity levels, can
be considered close to equilibrium for any time in density ramp experiments.

Recently, the heat and particle exhaust characteristics of the TCV tokamak
were modified[13, 14] by an in-vessel structures of solid graphite baffles
that form a divertor chamber of increased closure, to better decouple divertor
and main chamber regions. In this work, experiments were performed with an
open divertor (non-baffled), see Figure 3a), b), c) and d), and in the
presence of the first version of the baffles, see Figure 3e), f), g) and h).
The integrated ion flux does not roll over during the density ramps in the
absence of the baffles for these shots, see Figure 3 b), in contrast to the
baffled shots, with a roll over at $\langle n_{e}\rangle\lesssim 10\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$, see Figure 3f). Likewise, with
the baffles an earlier movement of the CIII front towards the X-point and a
substantially higher neutral divertor pressure (up to a factor $5$ higher) is
obtained for the same core conditions. These effects of the baffles are
similar, but even stronger than previous L-mode results obtained at
$I_{p}=250\leavevmode\nobreak\ \mathrm{kA}$ [13, 14].

Note that the gas flow required for fueling was lower for the baffled low
density discharge in Figure 2g) than for the non-baffled one. This isnot a
general observation with the gas flow in other experiments being often higher
with baffles installed. The result in Figure 2g) can be explained by the
dominant plasma fueling source coming from recycled neutrals, such that small
changes in the recycling coefficient, a property of the wall surface
condition, can substantially influence the required gas puffing rate.

##  3 Procedure for the interpretation of RDPA measurements

In this section, we describe how key quantities, such as the parallel ion Mach
number, electron density, ion flux along the magnetic field and the $E\times
B$ fluxes, are deduced from time averaged RPDA measurements. To illustrate
these steps, example results from RDPA in an attached L-mode plasma without
baffles, at a line-averaged density of $\langle n_{e}\rangle\approx 6.75\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$, and with same geometry and
experimental parameters as for the discharges in Figure 3 (unfavorable ion
$\vec{B}\times\nabla\vec{B}$ drift, $I_{p}\approx 320\leavevmode\nobreak\
\mathrm{kA}$) are presented in Figures 5 to 8.

The horizontal probe arm of the RDPA, shown in Figure 1b), is equipped [4]
with $12$ Mach probes, radially spaced by $10\leavevmode\nobreak\
\mathrm{mm}$, Figure 4. These probe tips can be operated at constant bias, in
voltage sweep, or in floating potential mode, similarly to the TCV wall-
embedded probes [15, 16]. Data is acquired at $2\leavevmode\nobreak\
\mathrm{MHz}$. When operated in swept mode, and for each probe tip, the ion
saturation current $J_{sat}$, the electron temperature $T_{e}$, and the
floating potential $V_{fl}$ are obtained from a $4$-parameter fit that takes
sheath expansion into account [15]. This is generally performed upon data
acquired during a $10\leavevmode\nobreak\ \mathrm{ms}$ period, equivalent to
$10$ voltage sweep periods for the typical sweep frequency of
$1000\leavevmode\nobreak\ \mathrm{Hz}$ and improves the data quality as
compared to using data from individual sweeps.

###  3.1 Parallel flow measurements.

Figure 4:  Sketch of the RDPA probe arm with embedded probes and their
position relative to the magnetic field: upstream or downstream. Figure 5:
RDPA measurements of a) Upstream ion saturation current density, b) Downstream
ion saturation current density, c) Mach number and d) Parallel particle flux
density. Each figure is divided into three regions: top) 1D profile obtained
with RDPA near the top of the plunge (in the region within the dashed red
rectangle near the X-point in the middle plot), middle) 2D contour plot from
RDPA and bottom) 1D profile near the bottom of the plunge (in the region
within the dashed red rectangle near the target in the middle plot). The blue
and green data in the bottom panels of a) and b) are obtained from the floor
LPs. Discharge #63029.

The parallel ion Mach number is deduced with RDPA from the ratio of upstream
to downstream $J_{sat}$ [17]:

$M=\ln(\frac{J_{sat1}}{J_{sat2}})/2.2.$ (1)

Here, $J_{sat1}$ and $J_{sat2}$ are obtained from swept probes or, for a
higher time resolution, with the probes operated in ion-saturation current
mode.

The electron density $n_{e}$, in the presence of flows, is calculated from a
viscous plasma model based on diffusive perpendicular transport [17]:

$n_{e}=\frac{J_{sat1}/e}{c_{s}\exp(-1+1.1M)},$ (2)

where $c_{s}$ is the plasma sound speed, usually calculated as
$\sqrt{(T_{e}+T_{i})/m_{i}}$ [15] with the assumption $T_{e}=T_{i}$. Unlike
the sign convention given in [17], here $M$ is defined as positive for a
particle flux directed towards the upstream probe tip and away from the
downstream probe tip. A positive Mach number, therefore, corresponds to a
plasma flow directed towards the target. Equation (2) shows reasonable
agreement with expressions typically used for density measurements with LPs in
the bulk plasma[18] and for $M=0$, as well as for measurements at the walls
(from wall-embedded probes) assuming $M=1$. For $M=0$, Equation (2) becomes:

$n_{e}=\frac{J_{sat1}/e}{c_{s}exp(-1)}\approx\frac{2.7J_{sat1}/e}{c_{s}},$ (3)

that agrees within $35\%$ with the usual expression[18]:

$n_{e}=\frac{2J_{sat1}/e}{c_{s}}.$ (4)

For $M=1$, Equation (2) becomes:

$n_{e}=\frac{J_{sat1}/e}{c_{s}\exp(0.1)}\approx 0.9\frac{J_{sat1}/e}{c_{s}},$
(5)

which is close to the commonly used formula for the sheath edge density:

$n_{se}=\frac{J_{sat1}/e}{c_{s}}.$ (6)

The density $n_{e}$ in Equations (3)-(5) is intended to represent the plasma
density of the unperturbed plasma (in the absence of the probe) and differs
from the sheath edge densities $n_{se1}$ and $n_{se2}$ on the upstream and
downstream probe tips. Another model, derived with drift based perpendicular
transport, gives a similar formula for the density [19]. The contributions
from perpendicular drifts (represented by the Mach number $M_{\perp}$
perpendicular to the magnetic field) to the calculated plasma density were
calculated with this drift based model [19]:

$n_{e}=\frac{J_{sat1}/e}{c_{s}\exp(-1-(M-M_{\perp}cot(\theta)))},$ (7)

where $\theta$ is the angle (in the plane of magnetic field and drift
velocity) of the object surface to the magnetic field and $M$ is defined here
with the sign convention given in [17]. As stated in [19]: ”If a facet lies in
a concave region of the object […], then it does not possess its own plasma
region. Instead, the solution(s) of the earlier region(s) applies right up to
the respective fractions of that facet.” and, therefore, the relevant angle
$\theta$ for the RDPA probe tip is not the angle of the probe tip surface,
because of the concavity of the RDPA cross-sectional geometry for a downward
$E\times B$ velocity. Instead, the angle between the boron nitride thermal
shield surface and the magnetic field direction [4], $\theta\approx
15^{\circ}$, is appropriate for Equation (7). The term $M_{\perp}cot(\theta)$
contributes a noticeably to the density calculation in the case of large
$E\times B$ velocities, such as for the experimental results shown in Figure 6
and 7 ($T_{e}\approx 27\leavevmode\nobreak\ \mathrm{eV}$, $v_{E\times
B}\approx 3000\leavevmode\nobreak\ \mathrm{ms^{-1}}$):

$M_{\perp}cot(\theta)=\frac{v_{E\times
B}}{c_{s}}cot(\theta)\leq\frac{3.7\times 3000\leavevmode\nobreak\
\mathrm{ms^{-1}}}{51000\leavevmode\nobreak\ \mathrm{ms^{-1}}}\approx 0.22$ (8)

This density correction, due to the perpendicular velocity, has not been
included in the present work and may lead to an error of up to $20\%$ in the
density calculation for the worst case (region of strong downward $E\times B$
velocity).

Finally, the parallel ion flux density is calculated as follows:

$\Gamma_{\parallel}=v_{\parallel}\cdot n_{e}=M\cdot c_{s}\cdot
n_{e}=\frac{MJ_{sat1}/e}{\exp(-1+1.1M)}.$ (9)

Note that the flow measurement is independent of the temperature measurement.
This is an advantage in the case of detached plasmas, where the electron
temperature can be overestimated for Langmuir probe measurements [15]. The
upstream ion saturation current collected by RDPA is usually similar to the
ion saturation current collected by wall probes, see the bottom panel of
Figure 5a). The downstream current is, however, usually a factor $2$ lower,
see Figure 5b), resulting in a Mach number, $M\approx ln(2)2)/2.2\approx 0.3$,
as shown in Figure 5c), that increases towards the target. An example of
parallel ion flow measurements based on Equation (9) is shown in Figure 5d).

###  3.2 $E\times B$ flow measurements.

$E\times B$ particle fluxes are calculated as the product between the local
plasma density and the $E\times B$ drift velocity:

$\vec{\Gamma}_{E\times B}=n_{e}\cdot\vec{v}_{E\times
B}=\frac{J_{sat1}/e}{c_{s}\exp(-1+1.1M)}\frac{\vec{E}\times\vec{B}}{B^{2}}$
(10)

The drift velocity is calculated from the plasma potential measurement
obtained from sheath theory:

$V_{pl}=(V_{fl,downstream}+V_{fl,upstream})/2+3T_{e,upstream},$ (11)

where $T_{e,upstream}$ is expressed in $[eV]$ and the constant $3$ corresponds
to a deuterium plasma (assuming $T_{e}\approx T_{i}$ and no secondary electron
emission [18]). Example measurements of these quantities are presented in
Figures 6 and 7. In the absence of a valid theory explaining occasionally
observed discrepancies between upstream and downstream floating potential
measurements, apparent in Figure 6c) and d), an average of the upstream and
downstream values is taken. This choice is motivated by a quantitative
agreement with the $V_{pl}$ target profiles, see Figure 7a), although it does
not address the discrepancies in upstream and downstream $V_{fl}$ seen near
the top of the plunge, where a comparison with wall LPs is not meaningful.

For electron temperatures, the difference between upstream and downstream
values is usually less pronounced than for the $V_{fl}$ profiles, see Figure
6a) and b). The upstream electron temperature value was chosen in the
calculations.

The electric field in the toroidal direction can be neglected as the loop
voltage, in steady state conditions, is small. For the case of a predominantly
toroidal field ($B_{z}$, $B_{r}\ll B_{\phi}$), the $E\times B$ drift velocity
can then be written as:

$\vec{v}_{E\times
B}\approx\frac{-E_{z}B_{\phi}}{B^{2}}\vec{e}_{r}+\frac{E_{r}B_{\phi}}{B^{2}}\vec{e}_{z}.$
(12)

The second term dominates in the case considered here, with a near-vertical
divertor leg and with stronger $V_{pl}$ variations across, than along, the
divertor leg. In Figure 7, example 2D measurements of $V_{pl}$, $E_{r}$, and
$\vec{v}_{E\times B}$ projected along the vertical direction are shown. The
vertical $E\times B$ velocity in Figure 7 is taken positive when directed
towards the target corresponding to a projection along the vector
$-\vec{e_{z}}$. This graphical choice provides the same sign convention as the
parallel ion flux in Figure 5d) (positive towards the target).

Figure 6:  Figure equivalent to Figure 5, showing RDPA measurements of a)
Upstream electron temperature, b) Downstream electron temperature, c) Upstream
floating potential and d) Downstream floating potential. The blue and green
data in the bottom panels of a) and b) are obtained from the floor LPs.
Discharge #63029. Figure 7:  Figure equivalent to Figure 5, showing RDPA
measurements of a) Plasma potential, b) Radial electrical field and c)
Vertical $E\times B$ velocity. Discharge #63029. Figure 8:  Figure equivalent
to Figure 5, showing RDPA measurements of a) Vertical particle flux density
from the parallel Mach measurement, b) Vertical $E\times B$ particle flux
density and c) Total vertical particle flux density. Discharge #63029.

A clear result from these measurements is that $E\times B$ flows, although
much weaker than parallel flows in the divertor, bring a substantial
contribution to the total poloidal ion flux due to the shallow pitch angle of
the field lines (field lines are near toroidal). This poloidal contribution
can be larger than that from the parallel flows, in the case of attached
discharges, Figure 8, where the high electron temperatures lead to steep
plasma potential profiles. A similar observation of strong $E\times B$ flows
was observed experimentally in DIII-D [7, 8, 9, 20].

###  3.3 Density fluctuations

Performing electron temperature, or even ion temperature, measurements at the
plasma turbulence timescale is not possible with the conventional single
Langmuir probe electronics used in this study. Density fluctuation
measurements are more accessible, as $J_{sat}\propto c_{s}n_{e}$ fluctuations
are generally dominated by density fluctuations [21, 22]. This can be
partially explained by the relatively weak dependence of $c_{s}$ on the
electron temperature (square root).

Density fluctuation levels are deduced here from the standard deviation of the
$I_{sat}$ time windows. The typical duration of a time window is chosen to be
approximately $1\leavevmode\nobreak\ \mathrm{ms}$ (equivalent to $2000$
acquired time points at a $2\leavevmode\nobreak\ \mathrm{MHz}$ frequency). The
time windows can be recorded while operating the probe in $I_{sat}$ mode or in
voltage sweeping mode, retaining only the intervals when the probe voltage is
sufficiently negative for the probe to record $I_{sat}$. In some regions, in
particular in the private flux region where signal levels are very low, the
$\widetilde{J_{sat}}$ and $\widetilde{n_{e}}$ signals (the tilde symbol stands
for their standard deviation) are dominated by instrumental noise. To correct
for this, the standard deviation of the noise is recorded before the plasma
discharge and then subtracted assuming that the signal and the noise are
independent random variables. The variance of the actual signal is thus
deduced as:

$\sigma_{signal}=\sqrt{\sigma_{measurement}^{2}-\sigma_{noise}^{2}}$ (13)

The density fluctuations are then derived from Equation (2):

$\widetilde{n_{e}}=\ThisStyle{\stackengine{-.1\LMpt}{\SavedStyle\left(\frac{J_{sat1}/e}{c_{s}\exp(-1+1.1M)}\right)}{\stretchto{\scaleto{\SavedStyle\mkern
0.2mu\AC}{.5}}{.3}}{O}{c}{F}{T}{S}},$ (14)

which we approximate as:

$\widetilde{n_{e}}\approx\frac{1}{\langle
c_{s}\rangle}\ThisStyle{\stackengine{-.1\LMpt}{\SavedStyle\left(\frac{J_{sat1}/e}{\exp(-1+1.1M)}\right)}{\stretchto{\scaleto{\SavedStyle\mkern
0.2mu\AC}{.5}}{.3}}{O}{c}{F}{T}{S}},$ (15)

where $\langle c_{s}\rangle$ is the time-averaged, local sound speed, obtained
from processing the time averaged data from swept probes. The normalized
fluctuation level is approximated as:

$\frac{\widetilde{n_{e}}}{\langle
n_{e}\rangle}=\ThisStyle{\stackengine{-.1\LMpt}{\SavedStyle\left(\frac{J_{sat1}/e}{\exp(-1+1.1M)}\right)}{\stretchto{\scaleto{\SavedStyle\mkern
0.2mu\AC}{.5}}{.3}}{O}{c}{F}{T}{S}}/\frac{\langle
J_{sat1}\rangle/e}{\exp(-1+1.1\langle M\rangle)}.$ (16)

##  4 Particle balance results in the divertor

In this section, we apply the RDPA data analysis presented in section 3 to
shed light on the divertor particle balance as a function of core density,
comparing discharges without and with baffles

###  4.1 The influence of core density on the divertor particle balance - no
baffles

Figure 9:  Sketch of the evaluation of the total ion flux to the outer target
obtained by integration in the radial and toroidal directions. The red curve
represents the vertical ion flux due to parallel and $E\times B$ flows. Figure
10:  1D divertor particle balance (left column) and peak $T_{e}$ (right
column) along the outer divertor leg for different core densities: a) Low core
density reference #65964 $\langle n_{e}\rangle\approx 5.0\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$, b) Intermediate core density
reference #66220 $\langle n_{e}\rangle\approx 8.4\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$ and c) High core density
reference #66222 $\langle n_{e}\rangle\approx 10.6\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$. Blue curves in the left column
show total vertical ion fluxes to the target due to parallel flows only, while
the red curves include the contribution from the $E\times B$ velocity. All
discharges without baffles.

We perform a 1D particle balance analysis along the divertor leg, obtained by
integrating the vertical ion flux densities due to parallel and $E\times B$
flows, obtained from the RDPA. The integration is performed both along the
radial and the toroidal directions. Thus, the result does not depend on
effects due to radial cross-field transport, as radial transport spreads the
profile but does not change the total poloidal ion flux along the leg. Only
source and sink terms, such as volumetric ionization and recombination, can
change it. Figure 9 shows an illustration of the integration, performed in the
relevant geometry.

Figure 10 shows data for three non baffled experiments with different core
densities. The data reproducibility between separate RDPA plunges is generally
good, as shown in Figure 10a), where $4$ curves from two up- and two down-ward
plunges are superposed.

The low density reference (Figure 10a)) has a non-negligible ion flux from the
upstream SOL (above the RDPA coverage),
$\iint\Gamma_{upstream}dS/\iint\Gamma_{target}dS\approx 20\%$. As the RDPA
does not reach to the X-point, it is possible that the real contribution from
the upstream SOL is close to zero or even negative (net flow of particles
towards the inner target through the common and/or the private flux regions).
The plasma shows a high peak electron temperature $T_{e,max}\approx
30\leavevmode\nobreak\ \mathrm{eV}$ and a small electron temperature gradient
along the divertor leg (Figure 10a), right panel), as expected from efficient
electron heat conductivity for this high electron temperature. This high
electron temperature and a relatively narrow radial profile width lead to an
interesting consequence: the $E\times B$ flow contribution to the poloidal
particle flux is greater than the one due to the parallel flow. As one could
expect from Bohm-Chodura sheath boundary conditions including drifts [18], the
parallel flow even reverses in the downward $E\times B$ region, pointing away
from the target along the divertor leg, near the separatrix, as shown in
Figure 11a).

Figure 11:  RDPA measurements for the low density reference without baffles
(shot 65964 in Figure 10a) of: a) Vertical particle flux density from the
parallel Mach number measurement and b) Vertical $E\times B$ particle flux
density.

In all non-baffled shots, the electron temperature ($T_{e,max}\geq
10\leavevmode\nobreak\ \mathrm{eV}$), e.g. Figure 10, is high enough to ionize
neutral particles along the entire divertor leg. This is consistent with the
CIII front position, that barely leaves the floor, as shown in the right
column of Figure 10. The intermediate core density and the high density
references, see Figure 10b) and c), have higher divertor ionization than the
low density case, attested by the steeper increase in the total ion flux
towards the floor and the higher flux measured by the floor probes. The
parallel ion flux even appears to slightly reverse near the top of the plunge
at the highest density and remains close to zero when including the $E\times
B$ drift contribution (Figure 10c). Overall, the small particle fluxes
entering the divertor from upstream agrees with a “closed box” divertor
approximation [10, 11], where most of the ionization is taken to occur in the
divertor. More studies are required in this regard on TCV, taking advantage of
upstream fast scanning probe measurements to determine the particle source
originating from the core and the upstream SOL.

###  4.2 The influence of core density on the divertor particle balance - with
baffles

Figure 12:  Equivalent to Figure 10 for baffled discharges: a) Low core
density references #64766 $\langle n_{e}\rangle\approx 5.2\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$, b) Intermediate core density
reference #64965 $\langle n_{e}\rangle\approx 10.3\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$ and c) High core density
reference #64962 $\langle n_{e}\rangle\approx 11.1\times
10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$ (beyond roll-over). Blue curves
in the left column show total vertical ion fluxes to the target due to
parallel flows only, while the red curves include the contribution from the
$E\times B$ velocity. Figure 13:  Low core density discharges without baffles
#65964 ($\langle n_{e}\rangle\approx 5.0\times 10^{19}\leavevmode\nobreak\
\mathrm{m^{-3}}$) and with baffles #64766 ($\langle n_{e}\rangle\approx
5.2\times 10^{19}\leavevmode\nobreak\ \mathrm{m^{-3}}$). a) Total ion flux to
the outer target including both parallel flow and $E\times B$ contributions
and b) Peak electron temperature value.

Figure 12 shows RDPA results (integrated ion flux and peak electron
temperature) for three baffled experiments with increasing core density. The
fraction of the target ion flux from the upstream SOL (above the RDPA
coverage) is $\iint\Gamma_{upstream}dS/\iint\Gamma_{target}dS\approx 15\%$ for
the low-density reference a). There is a high peak electron temperature at the
top of the plunge and a substantial temperature gradient from
$T_{e,max}\approx 25\leavevmode\nobreak\ \mathrm{eV}$ to $T_{e,max}\approx
12\leavevmode\nobreak\ \mathrm{eV}$. The CIII front position remains close to
the target, similarly to the non-baffled discharges.

The intermediate core density reference, Figure 12b), has the highest divertor
ionization and no significant ion flux from the upstream SOL. The parallel
flux is directed upwards (negative parallel flux) at the top of the RDPA
plunge and the total flux (including the $E\times B$ drift) is close to zero.
We note that the parallel flux is dominantly reversed in the region of
downward $E\times B$ velocity (not shown), which is close to the separatrix in
these discharges. The downward $E\times B$ transport plays a major role in the
upper region of the divertor leg, where the temperature radial gradient is
significantly higher than at the target. The electron temperature is marginal
to neutral ionization near the target. Consequently, the total ion flux
profile remains flat close to the target in the absence of a divergence term
in the region. This region is below the CIII front, which is located $\approx
13\leavevmode\nobreak\ \mathrm{cm}$ above the target in this case.

The high core density reference, Figure 12c), has a negligible divertor
ionization with the entire ion flux originating from the upstream SOL, above
the RDPA coverage. This is apparent from the nearly flat total vertical ion
flux profile along the entire outer divertor leg. The Mach number, not shown
here, is fairly constant across the entire profile and stays within $0.4$ to
$0.6$. The $E\times B$ transport contribution is smaller than the parallel
transport throughout the entire RDPA scan. In contrast to the other
discharges, the ion flux even slightly decreases towards the target, by
$\approx 20\%$ indicative of volumetric recombination. Indeed, both
spectroscopic studies [23] and SOLPS simulations [24] showed the presence of
modest levels of recombination for detached L-mode TCV plasmas. The
recombination probability exceeds that for ionization only below $T_{e}\approx
1.5\leavevmode\nobreak\ \mathrm{eV}$. However, molecular activated
recombination (MAR) has been suggested as a possible candidate to explain the
missing ion flux [25, 26] at higher electron temperatures, up to $T_{e}\approx
3\leavevmode\nobreak\ \mathrm{eV}$. Langmuir probe floor measurements indicate
$T_{e}\approx 6\leavevmode\nobreak\ \mathrm{eV}$ here. There is, however, the
possibility of over-estimation of $T_{e}$ by the LPs in detached conditions
[15], so the real value could be considerably lower. The CIII front is
$\approx 5\leavevmode\nobreak\ \mathrm{cm}$ below the X-point, beyond the RDPA
coverage in these discharges.

###  4.3 The effect of baffles for a fixed core density

The effect of the baffles on detachment onset, already shown in Figure 3, were
clearly mirrored in the particle balance shown in Figures 10 and 12. Here, we
contrast the lowest density discharges, for which a good match of the core
quantities was achieved, see Figure 2. Clear differences between the non-
baffled and baffled discharges appear only in the radiated power, the gas flux
required for fueling and the divertor neutral pressure. Bolometry indicates
that the increase in radiated power mainly originates from the divertor (inner
leg, outer leg and X-point region), whose lower temperatures and higher
densities with baffles can be expected to enhance both the carbon impurity and
hydrogenic radiated power. The carbon concentration for both discharges is,
however, unknown and may also be a key parameter in explaining the radiated
power difference.

This comparison clearly highlights the higher divertor ionization of the
baffled case, Figure 13a): more flux arrives at the target. Similar, or even
slightly smaller, fluxes arrive from upstream. Such higher ionization level is
expected [24] as the higher neutral density combined with sufficient plasma
temperatures lead to stronger ionization. Lower electron temperatures with
baffles is also apparent in Figure 13b).

##  5 Fluctuation results

Figure 14: Data from the low density non baffled shot #65964 and the high
density baffled shot #64965 to illustrate the density fluctuation profiles in
various condition: a) and d) time averaged electron density, b) and e):
standard deviation of the density and c) and f): relative density fluctuation
level (standard deviation normalized by the time averaged density).

We have shown how poloidal particle transport in the divertor contains strong
contributions from flows along the magnetic field and perpendicular to it, due
to steady state $E\times B$ drifts. A full description of the divertor
processes must, however, also include turbulence dynamics. Ongoing studies
combine numerical simulations [27, 28, 29, 30] and dedicated experiments,
including RDPA measurements.

While these studies will generate further exploration, the purpose of this
section is to provide a description of the fluctuation levels in the
discharges described in the previous sections. Discharges with a wide range of
divertor regimes are studied here: a strongly attached, low density, non-
baffled discharge (#65964 in Figures 14 a), b) and c)), and a high density,
baffled, discharge (#64965 in Figures 14d), e) and f)), which is at the onset
of detachment (note that these are the same discharges presented in Figure
10a) and Figure 13b)).

Figure 15:  a) Ion saturation current density time traces from the low density
shot without baffles #65964: signal from the upstream probe tips of the RDPA
Mach probes (the labels \raisebox{-.9pt} {1}⃝ to \raisebox{-.9pt} {4}⃝ and the
positions of the corresponding data point in the poloidal plane are shown in
Figure 14a)). b) Ion saturation current density time traces from the high
density shot with baffles #64965: signal from the upstream probe tips of the
RDPA Mach probes (the labels \raisebox{-.9pt} {1}⃝ to \raisebox{-.9pt} {4}⃝
and the positions of the corresponding data point in the poloidal plane are
shown in Figure 14d)).

In the low density example, relative density fluctuation levels are almost
constant along a flux surface in the divertor leg, Figure 14c). The data
reveals four distinct regions to facilitate the description, Figures 15a) and
14c): \raisebox{-.9pt} {1}⃝ The private flux region, characterized by a
relatively quiescent and faint plasma. \raisebox{-.9pt} {2}⃝ The proximity of
the separatrix, on the HFS of the electron temperature peak (region of strong
downward $E\times B$ drift in these reversed field discharges), where a high
fluctuation level is, surprisingly, observed, with $\widetilde{n_{e}}/\langle
n_{e}\rangle\approx 0.5$. The origin of this high fluctuation intensity is
unknown. \raisebox{-.9pt} {3}⃝ Near the electron temperature peak. The density
fluctuation level in this region is the lowest $\widetilde{n_{e}}/\langle
n_{e}\rangle\approx 0.1$. \raisebox{-.9pt} {4}⃝ To the LFS of the electron
temperature peak. The density fluctuation level increases gradually from
$\widetilde{n_{e}}/\langle n_{e}\rangle\approx 0.1$ to
$\widetilde{n_{e}}/\langle n_{e}\rangle\approx 0.25$ in the far SOL. The
higher fluctuation level in the far SOL, compared to region \raisebox{-.9pt}
{3}⃝, is believed to result from reconnection with upstream turbulence. This
reconnection process was recently shown in the far SOL of TCV in similar, low
collisionnality, discharges by simultaneously tracking convective cells with
the Gas Puff Imaging (GPI) diagnostic [31] and RDPA mapped along field lines.

In the high-density example, the turbulence behavior differs strongly from the
low collisionnality case. The relative fluctuation levels change along flux
surfaces, as shown in Figure 14f). The data is, once again, divided in four
regions, at different positions, to facilitate the description, Figure 15b)
and Figure 14f): \raisebox{-.9pt} {1}⃝ As in the low density reference, the
private plasma is characterized by a relatively quiescent region with very
little plasma. \raisebox{-.9pt} {2}⃝ Close to the separatrix, on the HFS of
the electron temperature peak, low fluctuation levels, compared to the low
density reference, of $\widetilde{n_{e}}/\langle n_{e}\rangle\approx 0.2$, are
observed. The narrow, high fluctuation level feature to the HFS of the $T_{e}$
peak, seen in the low-density reference, is thus absent with increasing
collisionnality. \raisebox{-.9pt} {3}⃝ The low fluctuation region near the
maximum of the $T_{e}$ profile present in the low-density case is absent for
these higher density conditions Indeed, in the near SOL region, close to the
X-point height, where fluctuations are believed to be related to the upstream
turbulence, fluctuation levels of $\widetilde{n_{e}}/\langle
n_{e}\rangle\approx 0.45$ are observed. This value drops to
$\widetilde{n_{e}}/\langle n_{e}\rangle\approx 0.2$ near the target. This drop
coincides with the electron temperature drop shown in Figure 12b) and the
associated increasing collisionality. \raisebox{-.9pt} {4}⃝ The far-SOL, where
turbulent events are much weaker.

These measurements thus clearly show how the divertor fluctuation behavior
strongly varies between attached and detached divertor conditions, both
radially and poloidally. The consequences of theses changes on divertor
turbulence transport and target profile broadening is an important subject for
future studies.

##  6 Conclusion

This study reports detailed 2D Langmuir probe measurements across a large part
of the divertor region in TCV. The measured quantities include plasma density,
temperature, potential and parallel Mach number. These are used to estimate
vertical particle flux densities associated both with parallel flows and
$E\times B$ flows to generate a particle balance in the divertor. This method
was applied to Ohmic L-mode plasmas in both baffled and non-baffled divertor
configurations. A range of divertor regimes were accessed by varying the
plasma line-averaged density. To access high-density conditions, all
experiments were performed at a relatively high plasma current of $\approx
320\leavevmode\nobreak\ \mathrm{kA}$ and with an unfavorable ion-grad B drift
direction to avoid H-mode transitions.

Baffles are found to substantially increase the divertor neutral pressure and
facilitate the detachment onset. These effects were similar but stronger than
recent experiments with a lower plasma current[13, 14]. Results from density
ramps and constant density discharges agree well, at corresponding densities,
in terms of the integrated ion flux, the CIII front position and the divertor
neutral pressure, allowing some reduction in the required number of
experimental discharges.

This study reveals that the contributions from the $E\times B$ drift to the
poloidal ion flux can be comparable, and sometimes larger, than that from the
ion flux along the magnetic field lines, consistent with reported observations
from DIII-D [7, 8, 9]. A detailed particle balance in the divertor reveals
that, in most cases, and with and without baffles, most of the particle flux
to the outer target results from ionization along the outer divertor leg. This
supports the closed-box approximation frequently used in detachment models
[10, 11] and previously inferred on TCV from spectroscopic measurements [32].
Close to detachment onset, in these reversed field conditions, the integrated
parallel particle flux can even “reverse” just below the X-point, i.e. ions
flow upstream along the magnetic field, while the total flow, including the
$E\times B$ drift, remains positive, i.e. directed towards the target. In the
most detached conditions, the divertor leg becomes too cold for any
significant ionization to occur. In this extreme case, achieved only with
baffles in these experiments, the entire particle source is located in the
proximity of, or even above, the X-point, and the flux along the divertor leg
can even slightly decrease as it approaches the target, ascribed to plasma
recombination. A close match between the attached and lowest density
discharges, with and without baffles, was achieved in terms of upstream
properties such as line-averaged density, that revealed a substantial increase
in the divertor ionization level with baffles. Additionally, divertor electron
temperatures were reduced by $\approx 35\%$.

Observations regarding divertor density fluctuation measurements in these
plasmas include the development of a poloidal gradient in the fluctuation
levels, with increasing collisionnality, and the surprising presence of a
narrow, high fluctuation level region in the downward $E\times B$ region for
strongly attached, reversed field discharges. Many future research avenues are
now available to further improve the description of the divertor fluctuation
properties using the RDPA such as: cross correlation with $J_{sat}$ and
$V_{float}$ signals using the split Mach tip configuration, the assessment of
the heat and particle profile spreading along the divertor leg, or the study
of the divertor fluctuation and time-averaged profile properties in advanced
divertor geometries.

##  7 Acknowledgments

This work was supported in part by the Swiss National Science Foundation. 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 author(s) 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. This work was
supported in part by the US Department of Energy under Award Number DE-
SC0010529.

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