# X-point and divertor filament dynamics from Gas Puff Imaging on TCV

C. Wüthrich1, C. Theiler1, N. Offeddu1, D. Galassi1, D.S. Oliveira1, B.P.
Duval1, O. Février1, T. Golfinopoulos2, W. Han2, E. Marmar2, J.L. Terry2, C.K.
Tsui3 and the TCV team4 1 École Polytechnique Fédérale de Lausanne (EPFL),
Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland,
2MIT Plasma Science and Fusion Center, MA-02139, Cambridge, USA,
3Center for Energy Research (CER), University of California San Diego (UCSD),
USA,
4See the author list of H. Reimerdes et al 2022 Nucl. Fusion 62 042018
<EMAIL_ADDRESS>
###### Abstract

A new Gas Puff Imaging (GPI) diagnostic has been installed on the TCV tokamak,
providing two-dimensional insights into Scrape-Off-Layer (SOL) turbulence
dynamics above, at and below the magnetic X-point. A detailed study in L-mode,
attached, lower single-null discharges shows that statistical properties have
little poloidal variations, while vast differences are present in the 2D
behaviour of intermittent filaments. Strongly elongated filaments, just above
the X-point and in the divertor far-SOL, show a good consistency in shape and
dynamics with field-line tracing from filaments at the outboard midplane,
highlighting their connection. In the near-SOL of the outer divertor leg,
short-lived, high frequency and more circular (diameter$\,\sim\\!15$ sound
Larmour radii) filaments are observed. These divertor-localised filaments
appear born radially at the position of maximum density and display a radially
outward motion with velocity $\approx\\!400\,$m/s that is comparable to radial
velocities of upstream-connected filaments. Conversely, in these discharges
($B\times\nabla B$ pointing away from the divertor), these divertor filaments’
poloidal velocities differ strongly from those of upstream-connected
filaments. The importance of divertor-localised filaments upon radial
transport and profile broadening is explored using filament statistics and in-
situ kinetic profile measurements along the divertor leg. This provides
evidence that these filaments contribute significantly to electron density
profile broadening in the divertor.

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  *

##  1 Introduction

In a tokamak, the plasma core is magnetically confined on closed magnetic
field lines. However, heat and particles are continuously lost into the
Scrape-Off Layer (SOL), i.e. the region with open magnetic field-lines,
through cross-field transport. In the SOL, this exhaust heat is transported
primarily along these open magnetic field lines towards a narrow region of the
Plasma Facing Components (PFC), called the divertor target. One of the key
challenges for next generation fusion devices, such as ITER and DEMO, is in
handling this exhaust power [1, 2, 3]. If unmitigated, peak target heat fluxes
are predicted to exceed material limits , resulting in excessive erosion and
melting of the PFCs.

Turbulent transport, predominantly manifested in the form of intermittent
structures named filaments [4], is believed to often be the dominant
contribution to SOL cross-field transport, especially in the far-SOL [5].
Convective radial transport associated with filaments, also called blobs
because of their shape perpendicular to the magnetic field, has been shown to
carry substantial fraction of the power $P_{SOL}$ crossing the Last Closed
Flux Surface (LCFS) into the far-SOL [6]. Phenomena such as the far-SOL
density shoulder along with high levels of potentially harmful plasma
interaction with the main chamber first wall have also been associated with
filament dynamics [7, 8, 9]. These structures can extend along the magnetic
field lines into the divertor [10, 11]. Their radial velocity, SOL penetration
distance and the density and heat carried by the filaments, can also
significantly determine the target heat and particle flux width [7].

Filament generation and dynamics have been extensively studied at the low
field side outboard midplane of various tokamaks [12], such as ASDEX-U [7],
NSTX [13], Alcator C-Mod [14], DIII-D [15], MAST [16] and TCV [17, 8, 11].
Considerably less is, however, known about the properties of filaments around
the magnetic X-point and in the divertor. A disconnection is expected in the
vicinity of the X-point due to flux tube squeezing due to strong flux
expansion and magnetic shear [4, 12]. Radial $\vec{E}\times\vec{B}$ shear may
act as an additional disconnection mechanism, impacting filaments of larger
poloidal sizes depending on the temperature $T_{e}$ and poloidal field $B_{p}$
[18, 11]. A better understanding of this is of great importance, as turbulent
transport in this region may contribute to the spreading of heat and particle
radial profiles along the divertor leg [19]. Gas Puff Imaging (GPI)
measurements on C-Mod in the region above the X-point showed elongated shapes
with increased radial velocities compared to the outboard midplane [20].
Filament motion around the X-point, both radially and poloidally, has been
seen to vary with $B\times\nabla B$ direction on Alcator C-Mod [21]. Fast
visible imaging on MAST [22, 23] and NSTX [10] portrayed a complex picture of
filaments entering the divertor forming three different regions of turbulence
(PFR, near- and far-SOL common flux). A quiescent region was observed in the
near-SOL around the X-point and down to the target plates, together with the
existence of small scale filaments intrinsic to the divertor. Those appeared
connected to the target and field-aligned up to the X-point, where they
poloidally disconnect. Radial and poloidal sizes of these divertor filaments
of the order of $1$-$3$ cm were observed and related to resistive-ballooning
modes in the bad curvature region of the outer divertor.The lack of local
radial velocity measurements did not, however, allow to draw any conclusions
on their contribution to radial particle and heat fluxes.

A detailed experimental description of the fluctuation properties in the
X-point and divertor region improves evaluation of heat and particle
redistribution in the divertor, but is also of primary importance for model
validation of turbulence codes. These could, in particular, improve predictive
capabilities of the heat flux scale lengths at the target plates that are
among the most critical issues for successful operation of ITER and DEMO [2].
Disentangling the different turbulent mechanisms has recently advanced
significantly [24, 25] and real-size, global turbulence simulations of
diverted discharges are within reach as demonstrated for MAST [26], ASDEX-U
[27] and TCV [28]. Systematic simulation-experimental validation was recently
performed for X-point geometries on TORPEX [29] and TCV [28]. They revealed
strong differences in filament dynamics between the codes and experimental
measurements in the X-point and divertor region, which calls for further
studies. The detailed nature of radial transport in the divertor is also a key
missing component in the performance prediction of long legged, tightly-
baffled, divertor scenarios [30] that show large promise for safe power
exhaust in reactors.

This paper describes the filamentary transport properties at multiple poloidal
locations in TCV, focusing on the dynamics around the X-point and along the
outer divertor leg of Lower Single-Null (LSN) discharges. A new diagnostic gas
puff in the vicinity of the X-point on TCV provides two-dimensional
measurements of SOL turbulence properties, focusing upon filament appearance
and dynamics, with high spatio-temporal resolution. The paper is organised as
follows: The diagnostic together with its technical characteristics are
described in sec. 2 with a description of the performed discharges on TCV
following in sec. 3. In sec. 4, several statistical moments are discussed
across multiple poloidal locations with several diagnostics before analysing
in sec. 5 filament shapes and dynamics around the X-point from the X-point
GPI. An estimate of their contribution to cross-field transport is presented
in sec. 6 together with the measurements of 2D density and temperature
profiles in the divertor.

##  2 X-point GPI system

###  2.1 Hardware description

The Tokamak à Configuration Variable TCV (major radius $R_{0}$ = 0.88 m,
toroidal field $B_{T}\leq 1.45$ T) [31] is equipped with many edge turbulence
diagnostics. Over 180 wall-embedded Langmuir Probes (LP) [32, 33], a
reciprocating probe (RCP) [8] at the outboard midplane and a Reciprocating
Divertor Probe Array (RDPA) [34] allow for 1D and 2D fluctuation measurements
of ion saturation current, floating potential and parallel Mach number in the
midplane SOL and divertor, respectively. GPI provides 2D turbulence imaging at

Figure 1: TCV X-point GPI system. CAD image of the gas injection system in
sector 6 of TCV, with the gas puff in the tip of a LFS baffle tile. The
X-point GPI viewing geometry and camera Field of View (FoV) is illustrated in
cyan. A typical plasma separatrix at the toroidal angle of the gas puff is
shown in red. A raw image acquired with this setup is shown on the right.
Certain parts of the FoV are discarded due to low Signal-To-Noise Ratio (SNR)
or baffle shadowing. The crosses indicate the CAS trigger locations.

the outboard midplane of TCV [35, 11]. However, turbulence imaging in the
X-point region was limited up to now.

For this reason, a new GPI system was designed (fig. 1) to obtain insights
into the turbulence dynamics across an extended poloidal region around the
magnetic X-point of Lower Single Null (LSN) plasmas. Key properties are
illustrated here but further diagnostic details will be presented in [36].
Part of TCV’s Plasma Exhaust (PEX) upgrade included the installation of baffle
tiles on both the Low-Field-Side (LFS) and High-Field-Side (HFS) to separate
the main chamber from the divertor [37]. Further to its main purpose of
studying neutral compression and simplified detachment access [38, 39], a
capillary for neutral gas injection was installed in the LFS baffle tip (R
$\approx\\!0.954$ m, Z $\approx\\!-0.365$ m) in the vicinity of the X-point.
Gas is injected horizontally into the vessel from a single nozzle with a flow
rate of $\approx 6\cdot 10^{19}$ at/s and a distance to the separatrix of
typically 10-15 cm, depending on the target plasma geometry. The capillary
tube (blue in fig. 1) runs behind the graphite tiles to the bottom of the
vacuum vessel, where a feedback controlled piezoelectric valve controls the
flow rate. Helium (He) gas puffs were used in all of the discharges described
in this work, though the system also permits for deuterium (D2) injection.
This was chosen as the background light emission from D2 can be orders of
magnitude higher than at the outboard midplane, displaying significant
emissivity and reduced toroidal localisation of the light from the GPI
injected neutrals [40].

Figure 2: Schematic illustration of the fast-imaging Phantom camera and its
mounting system on MANTIS. It views the first channel without disturbing the
other spectral cameras (the orange dashed arrow shows the reflected light
passage to the rest of MANTIS).

A magnetically shielded Phantom v2012 high speed camera ($400$ kHz, exposure
time $2\,\upmu$s, resolution of 126$\times$96 px2) is
used.111https://www.phantomhighspeed.com/products/cameras/ultrahighspeed/v2012
The camera was introduced into the Multispectral Advanced Narrowband Tokamak
Imaging System (MANTIS) [41], as shown in fig. 2, installed on TCV on the
lower tangential port of sector 8, with the light relayed from the port
through a set of mirrors and relay optics to a HeI 587.5 nm filter (2 nm
bandwidth, 95% transmission). This allows for the camera to be farther from
TCV, minimising any magnetic field influence while avoiding optical fibres.

An absolute spectral calibration allows for measurements of the local
emissivity. Each camera pixel collects light from a 1.9$\times$1.9 mm2 region
in the poloidal plane at the injection nozzle. The diagnostic Lines-Of-Sight
(LOS) are well aligned with the magnetic field in the gas puff plane, with a
poloidal and toroidal misalignment of $\approx\,$5∘and $\approx\,$3∘,
respectively, for discharges with standard helicity ($I_{p}$ same sign as
$B_{T}$) and geometries as those studied in this work. The toroidal gas cloud
extent along the magnetic field lines was estimated to be 5-10 cm, depending
on the distance to the nozzle. This results in a limiting resolution of $\leq
7$ mm as estimated using the approach in sec. II.E. in [40]. Smearing due to
the integration time of $2\,\upmu$s can add up to 2 mm to this limit for
cross-field velocities of 1 km/s. The position calibration of the pixel views
in the poloidal plane is performed using calcam raytracing [42] and typically
results in an uncertainty of 1 pixel.

###  2.2 Signal analysis and relation to density fluctuations

The brightness $I$ measured by the GPI camera detector in combination with an
adequate brightness calibration can be related to plasma parameters as [40,
43]

$I=\frac{1}{4\pi}\int_{LOS}n_{n}f\,\,dl\simeq\frac{1}{4\sqrt{\pi\ln{2}}}L\,n_{n}^{max}n_{e}^{\alpha}T_{e}^{\beta}$
(1)

with $n_{n}$ the injected neutral density available for excitation at the
observed wavelength and $n_{e}$ and $T_{e}$ the local electron density and
temperature, respectively. $\int_{LOS}dl$ depicts the integral along the
optical LOS of each pixel through the neutral gas cloud. For the approximate
expression on the right of eq. 1, a Gaussian profile for $n_{n}$ along the LOS
was assumed, with a peak value of $n_{n}^{max}$ and a half width half maximum
$L$, of sufficient narrowness that $n_{e}$ and $T_{e}$ may be considered
constant. $f(n_{e},T_{e})$ represents the ratio of neutrals in the upper
excited state of the radiative transition to the ground state times the rate
coefficient of this decay and is commonly rewritten as a power law function
with exponents $\alpha=\alpha(n_{e},T_{e})$ and $\beta=\beta(n_{e},T_{e})$
[40]. Such a dependence makes the relation between plasma parameters and GPI
intensity fluctuations non-linear and complicated.

A measure of the relative fluctuation amplitude can be obtained by normalising
the brightness to the moving average of the signal as

$\displaystyle S=\frac{I-\langle I\rangle_{1ms}}{\langle I\rangle_{1ms}}$
$\displaystyle\sim\frac{n_{n}(n_{e}^{\alpha}T_{e}^{\beta}-\langle
n_{e}^{\alpha}T_{e}^{\beta}\rangle)}{n_{n}\langle
n_{e}^{\alpha}T_{e}^{\beta}\rangle}$ (2)
$\displaystyle\approx\alpha\frac{n_{e}-\langle n_{e}\rangle}{\langle
n_{e}\rangle}+\beta\frac{T_{e}-\langle T_{e}\rangle}{\langle T_{e}\rangle}$
(3)

where $\langle I\rangle$ describes the moving average of the pixel-wise
brightness over typically 1 ms. Slow fluctuations of the neutral density, low
frequency plasma fluctuations and other effects due to cloud non-uniformity
are removed in this procedure [40]. $S$ is thus a quantity proportional to the
relative density and temperature fluctuations. Eq. 3 is valid only for small
fluctuations relative to the mean values of $n_{e}$ and $T_{e}$ (see also
[44]). For the investigated plasmas with $n_{e}\in[0.3,1]\cdot 10^{19}\,$m-3
and $T_{e}\in[5,25]$ eV, one expects $\alpha\in[0.4,0.6]$ and
$\beta\in[0.3,4]$ according to [40]. For this parameter range, we have
$\alpha(n_{e},T_{e})\simeq\alpha(n_{e})$ and
$\beta(n_{e},T_{e})\simeq\beta(T_{e})$ resulting in an approximately linear
dependence.

###  2.3 Image processing

In the diagnostic setup described above, the upper part of the FoV looks at
the underside of the LFS baffle, resulting in the shadowed area indicated in
the example image on the right of fig. 1. The corresponding pixels should not
be employed. Regions of the view with a SNR below 12 are also excluded, where
the SNR is evaluated as the ratio between the mean intensity during stationary
gas injection and the standard deviation $\sigma_{dark}$ before the gas puff,
where in the peak signal region, a SNR$\sim 60$-$80$ is typically observed. In
the remainder of this work, images recorded on the camera are horizontally
mirrored, such that the LFS region is located to the right, as is generally
the practice.

The image series are mostly analysed using Conditional Average Sampling (CAS)
[40] with a triggering threshold of $S>2.5\sigma$. A total of 81 trigger
locations are distributed over the FoV, as shown in fig. 1. The average radial
and poloidal velocities of the filaments at these locations are then extracted
from the Centre of Light (CoL) displacement, averaged over 5 CAS frames.

##  3 TCV L-mode scenarios

Figure 3: The three similar, but vertically displaced magnetic LSN geometries
considered in this work, together with the edge turbulence diagnostic
positions: the X-point and midplane GPI FoV (black and lila rectangle), the
RDPA (grey structure) and wall-LPs (red dots). The blue dots indicate the
measuring volumes of the Thomson Scattering (TS). The colour coding for GPI
data is maintained throughout this paper: red for data obtained from the lower
core, green from below the X-point and yellow from the outer divertor leg.

This work focuses on TCV lower single null, low density, L-mode configurations
($B_{T}=1.4$ T, $I_{p}=245$ kA, line average density $\approx\\!3.9\cdot
10^{19}$ m-3, Greenwald fraction $f_{G}\\!\approx\\!0.23$) with magnetic
geometry as shown in fig. 3. The figure also indicates the locations of the
used turbulence diagnostics. The discharges are performed in reversed field,
i.e. with the ion B$\times\nabla$B direction chosen to reduce H-mode access.
The plasma is fuelled from the top into the main chamber to avoid effects from
the baffles. An identical plasma was vertically displaced by $\pm 15$ cm
compared to the central case (green), for turbulence measurements with the LFS
X-point GPI probing a region above and below the X-point. An identical
discharge (#71575) to #70340 (red geometry in fig. 3) but in non-standard
helicity ($I_{p}=-245$ kA) is added for better alignment with the sight lines
of the outboard midplane GPI system. The connection length from the outboard
midplane to the outer target varies by $\pm 15\%$ across the three geometries
in fig. 3. Other relevant plasma parameters, such as triangularity, target
flux expansion ($f_{x}\approx 3.5$) and strike point position, were
essentially kept constant.

Displacing the plasma is, therefore, taken as a good approximation, to moving
the GPI view for turbulence measurements. In the following, these measurements
are super-imposed onto the green geometry in fig. 3 by vertical translations.
This approach is further supported by fig. 4, showing the electron density
$n_{e}$ and temperature $T_{e}$ profiles from TS in the lower half of the core
together with the floor LP profiles of the same quantities. Minimal
differences are observed both in the upstream SOL and at the floor, indicating
a weak impact of the outer divertor leg length on the measurements for these
plasma conditions.

A leading theory for filament propagation is the two region model [45]. Using
the $n_{e}$ and $T_{e}$ profiles from TS in fig. 4 and the midplane GPI data,
following the procedure in [11], we conclude these discharges to be in the
Resistive X-point regime. In such a regime, it is postulated that the ion
polarisation current is the dominant current return path, that occurs around
the X-point due to strong filament squeezing. Whether the current closure
occurs past the X-point or not depends on the collisionality.

a)b)c)d) Figure 4: Kinetic radial plasma profiles from the three equilibria in
fig. 3 of $n_{e}$ and $T_{e}$ from TS (a-b) by considering only the chords in
the lower half of the vessel. The normalised flux coordinate $\rho_{\Psi}$ is
defined as $\sqrt{(\Psi-\Psi_{0})/(\Psi_{LCFS}-\Psi_{0})}$, with $\Psi_{0}$
and $\Psi_{LCFS}$ the poloidal magnetic flux on-axis and at the LCFS,
respectively. The same quantities are extracted from wall-embedded LPs (c-d)
on the outer divertor target.

##  4 Statistical moments of fluctuations

Before focusing specifically on filaments, we investigate here the fluctuation
characteristics by looking at the first three statistical moments of the
measured brightness intensity $I$.

The 2D measurement of these quantities in the different regions around the
X-point, are shown in fig. 5. The computation is made piece-wise over a moving
4 ms time window before taking the mean over the full window to average low
frequency components. Diagnostic-related noise fluctuations are reduced by
subtracting the standard deviation before the He gas puff, $\sigma_{dark}$,
from that during the measurement window ($\sigma_{meas}$). Likewise, the
background brightness before injection, $\mu_{dark}$, is subtracted and an
analysed relative fluctuation level is deduced as
$\sigma=\frac{\sqrt{\sigma_{meas}^{2}-\sigma_{dark}^{2}}}{\mu-\mu_{dark}}$.

The mean brightness, fig. 5a, increases from the injection nozzle towards the
region of higher plasma density, reaching a maximum just before the LCFS in
all three probed regions. In the divertor leg, the maximum brightness
coincides well with the peak electron density according to fig. 4c. Beyond the
separatrix, the signal decreases rapidly, either due to low plasma density in
the PFR or from ionisation of injected neutrals in the plasma core. The
standard deviation (fig. 5b) shows a similar behaviour.

a)b)c)d) Figure 5: Statistical moments of GPI brightness (from a to d): mean
$\mu$ and standard deviation $\sigma$ in arbitrary brightness units, relative
fluctuation level $\sigma/\mu$ and skewness. The blue dashed lines indicate
flux surfaces with $\rho_{\Psi}\\!=\\![0.98,1.02,1.04,1.06]$ and the red line
the separatrix. Remarkable uniformity in $\sigma/\mu$ is observed for
$\rho_{\Psi}\in[1.01,1.03]$. $\sigma/\mu$ broadens around $\rho_{\Psi}\approx
1.06$ at the height of the X-point.

The relative fluctuation amplitude $\sigma/\mu$ (fig. 5c) shows a remarkable
poloidal uniformity over the entire measurement region in the near SOL and
throughout the divertor. It increases radially monotonically up to $\sim
80\,\%$ at $\rho_{\Psi}\approx 1.06$-$1.08$. At the divertor entrance,
however, a transition is observed in the far-SOL, resulting in a broadening of
the zone of low fluctuations. A decrease of $\approx$ 0.2 is observed for
$\rho_{\Psi}\\!\approx\\!1.06$ from just above to just below the X-point, with
no significant further poloidal variation along the divertor leg. The region
of $1.01\\!<\\!\rho_{\Psi}\\!<\\!1.02$ shows the lowest fluctuation level of
$\sim\,$10%, corresponding to the radial location of maximum density,
reminiscent of a quiescent region observed on MAST [22]. In the PFR and in the
core above the magnetic X-point, fluctuations remain low.

The skewness (fig. 5d) shows a similar poloidal uniformity. In contrast to
$\sigma/\mu$, no significant poloidal variation is observed in the far-SOL
above and below the X-point. Around the region of minimum $\sigma/\mu$, the
skewness becomes close to zero and even negative in the divertor leg. A radial
increase to $\approx\\!1.5$ at $\rho_{\Psi}\\!\approx\\!1.08$ is observed,
indicative of enhanced filamentary activity. Striations are observed in the
far-SOL skewness, consistent in size and tilt with typically observed
elongated filaments in this region, further discussed in section 5. Such
striations were also previously reported using passive fast imaging analysis
on MAST [22].

Figure 6: Radial profiles of rel. fluctuation level (top) and skewness
(bottom) for all X-point GPI locations as compared to the outboard midplane.
Also shown are the relative $J_{sat}$ fluctuations from RDPA in the outer
divertor leg of discharge #70340, at the same vertical distance to the X-point
($D_{xpt}$) as the GPI data labelled ”below X-point”.

These fluctuation measurements are now compared to GPI at the outboard
midplane. In fig. 6, radial profiles of $\sigma/\mu$ and skewness as a
function of $\rho_{\Psi}$ are shown. In addition, $J_{sat}$

a)b)c)d)e) Figure 7: False colour raw image sequence of discharge #70644
viewing below the X-point in the divertor leg. Every third frame is shown for
better visibility of the structures. The red line shows the separatrix and
blue dashed lines indicate flux surfaces at
$\rho_{\Psi}=[0.98,1.02,1.04,1.06]$, a convention followed throughout this
paper.

fluctuations measured by the RDPA in the divertor volume at a distance of
$D_{xpt}\,\approx\,15$ cm from the X-point are displayed.

This shows well the decrease of $\sigma/\mu$ from above to below the X-point
in the far-SOL but also a slight increase around $\rho_{\Psi}\,\approx\,1.03$
in the divertor near-SOL. At the outer-midplane, fluctuations are
significantly larger, by $\approx 0.3$ in the near-SOL. This suggests more
turbulence at the transition from open to closed magnetic field lines at the
outer midplane. The skewness is also higher at the outboard midplane compared
to the other poloidal regions, at least in the near-SOL for $\rho_{\Psi}\leq
1.04$.

The cross-comparison of RDPA (black curves in fig. 6) and the X-point GPI at
the same location (green curve) shows good agreement in both statistical
quantities for $\rho_{\Psi}\in[1.01,1.05]$. Discrepancies are observed in
relative fluctuation level radially further out. This could be related to the
difference in power dependence on $n_{e}$ and $T_{e}$ between the ion
saturation current measured by the RDPA and the He line emission intensity
from GPI. A comparison between LPs on the floor and GPI at the outer midplane
on C-Mod [44] showed similar trends with differences of up to 0.3 in
$\sigma/\mu$ in the far-SOL. The same effect could, to some extent, explain
the difference in the far-SOL between the midplane GPI, where neutral D2 is
puffed, and the X-point GPI using He injection. The two gases have different
$n_{e}$ and $T_{e}$ dependencies in line emission intensity (eq. 1). Previous
experiments with identical discharges measured with the midplane GPI on TCV,
once with D2 and once with He, showed agreement in the near-SOL and an
increase of 0.1 with He in the far-SOL.

##  5 Filament properties around X-point

In this section, we discuss 2D shapes, origin and velocities of filaments
observed by the X-point GPI. A series of raw GPI snapshot images over 30$\upmu
s$ from below the X-point, displayed in fig. 7, shows many characteristic
image features. As seen in the mean statistical moment (fig. 5a), the
brightest region is located at and just outside the separatrix. Two distinct
types of structures appear. Highly elongated structures are observed in the
far-SOL at $\rho_{\Psi}>1.04$, moving radially outwards and poloidally in the
direction of the target. In contrast, a more complex fluctuation pattern is
observed closer to the separatrix at $1.01<\rho_{\Psi}<1.05$. Multiple
structures, smaller in size, appear along the leg at several positions,
seemingly detaching from the brightest area and then moving towards the LFS.
To the left of the peak brightness region, in the PFR, no significant
fluctuations or filaments are identified all along the FoV. Thin, poloidally
elongated filaments in the PFR, as documented on C-Mod [21] and MAST [23],
were not detected here.

The snapshot series of the normalised signal $S$ (eq. 2) in fig. 8 provides
further insight. Just above the X-point, panels a)-e), clear structures are
visible in the SOL starting at $\rho_{\Psi}\approx 1.01$, followed by a radial
outwards displacement. Regularly, multiple filaments are visible
simultaneously within the observation window and they often shear apart in the
far-SOL around $\rho_{\Psi}\approx 1.06$ (d). Stronger poloidal motion is
observed closer to the LCFS together with less distinct filament like
features. Overall, the pattern above the X-point agrees well with GPI studies
on C-Mod [20].

a)b)c)d)e)f)g)h)i)j)k)l)m)n)o) Figure 8: Image sequences of normalised GPI
brightness $S$, above the X-point and in the divertor. In the two lower
regions, both elongated filaments in the far-SOL and circular structures in
the divertor leg are present. The green and black dotted contours correspond
to the half maximum contours from conditionally averaged filaments, with a
time separation of $\approx 16\,\upmu$s, detected with the midplane GPI in
discharge #71575. They are traced along magnetic field lines to the X-point
regions as shown in the magnetic reconstruction on the left.

In the region below the X-point, panels f)-j), as already noted, two regions
can be distinguished. The structures in the far-SOL have a large aspect ration
and show a near vertical tilting with strong fluctuation amplitude.
Independently, smaller scale and less intense filaments are observed from
$D_{xpt}\approx\,13$ cm below the X-point onwards. In the bottom window
(panels k-o) splitting and complex interactions between filaments can be seen.
They are present all along the divertor leg and can travel across the full
common flux width. Beyond $\rho_{\Psi}>1.06$, poloidally elongated features
are still occasionally observed.

These TCV divertor observations are consistent with the theoretical picture
elongated cross-sections of SOL filaments around the X-point region due to
increased flux expansion and magnetic shear [4], discussed further in sec.
5.1. The picture shown here also largely mirrors passive fast imaging
measurements on MAST [23, 22].

###  5.1 Magnetic mapping and identification of divertor localised filaments

Magnetic field line tracing [11] is used to identify the filament types in the
LFS poloidal locations and their possible upstream connection. Two CAS
contours are taken from the midplane GPI (indicated in green and black in the
top left of fig. 8) corresponding to a filament displacement over 16 $\upmu$s.
These contours are traced along the magnetic field lines down to the LFS outer
divertor views. The field lines intersect with the GPI views above and below
the X-point after $\sim$ 0.5 and 1 toroidal turns, respectively.

The dimension, tilt and location of the structures just above the X-point and
in the divertor far-SOL are well matched by shapes expected from upstream. The
typical time scale of the filament passage and the displacement direction also
agree fairly well in both regions. This provides strong evidence that these
structures are connected to upstream filaments for these plasma conditions.
The rarer observation of elongated filaments in the far-SOL of the lowest
divertor view shows that upstream filaments remain connected deep into the
divertor in the far-SOL. This observation is consistent with the high
correlation between divertor and midplane fluctuations observed in
magnetically connected positions [11]. The present measurements further show
that the midplane filaments do not necessarily reach the outer target at all
radial locations.

Indeed, the small scale turbulence in the divertor leg can not be attributed
to filaments above the X-point. Mapping their locations and CAS contours along
magnetic field lines above the X-point would result in poloidally elongated
ribbons with sizes around the ion sound gyro radius. However, no structures
with corresponding tilts and shapes are observed above the X-point. There is
clear evidence that these structures are localised in the divertor and do not
exist above the magnetic X-point. This would explain the low correlation of
fluctuations along the magnetic field lines between the midplane and the
divertor near-SOL, observed in comparable scenarios [11].

(a)

(b)

(c)

(d)

Figure 9: Shapes of 2D filaments observed in CAS trigger locations at the
outboard midplane a) and above the X-point on $\rho_{\Psi}\approx 1.035$ b).
Filaments in the divertor near-SOL c) at $\rho_{\Psi}\approx 1.035$ and in the
far-SOL d) $\rho_{\Psi}\approx 1.06$ are alos shown. For each case, the long
and short edge size ($\epsilon_{l}$ blue line and $\epsilon_{s}$ red line
resp.) is specified. The black dashed contour in b) and d) corresponds to the
field-line tracing of the midplane contour in a).

The filament sizes are quantitatively discussed in fig. 9 , where the sizes of
typical filaments are extracted from the CAS frames at typical trigger
locations in each region. Two characteristic sizes can be taken from the half
maximum contour: the longest extent $\epsilon_{l}$ and the corresponding
perpendicular edge $\epsilon_{s}$ passing through the filaments centre of
mass. While filaments at the outboard midplane (a) are elongated,
approximately, poloidally with $\epsilon_{l}\\!\sim 30\,\rho_{s}$, the
filaments just above the X-point (b) are elongated mostly radially with a
similar $\epsilon_{l}$. In the far-SOL below the X-point (d), the long edge is
tilted by magnetic shear, aligning almost with the poloidal direction. They
are less compressed ($\approx\,50\,\%$ larger $\epsilon_{s}$ and 30% smaller
$\epsilon_{l}$) than the mapped CAS contours from the outboard midplane (black
dashed contour). From the toroidal curvature and the LOS misalignment effects,
discussed in sec. 2, the radial enlargement remains, however, within the
diagnostic uncertainty of $\sim 5$-$6$ mm. The ion sound gyro-radius
$\rho_{s}\,=\,\frac{c_{s}}{\omega_{ci}}=$ $\frac{\sqrt{2T_{e}m_{i}}}{eB}$
$\approx 0.7$ mm (assuming $T_{e}\,\approx\,T_{i}$ $\approx\,15$ eV with ion
cyclotron frequency $\omega_{ci}$, ion sound speed $c_{s}$) is shown for scale
comparison. Typical divertor localised filaments, (c), have dimensions
$\sim\,15\rho_{s}$, that are comparable to estimates using line integrated
fast imaging on MAST [46].

As shown in fig. 10 a, the filament aspect ratio
$\epsilon_{l}/\epsilon_{s}\lessgtr 3$ provides a good measure to differentiate
filaments in the divertor. $\epsilon_{l}/\epsilon_{s}$ increases towards the
X-point reaching values of 8 in the far-SOL below the X-point. The transition
to predominantly more circular, divertor-localised filaments does not appear
bound to a flux surface, but rather increases radially beyond a poloidal
distance $D_{xpt}\approx 13$ cm from the X-point. In the lowest observation
window, only a few trigger locations at $\rho_{\Psi}\\!\geq\\!1.06$ show
elongated filaments. Whether the radial domain governed by divertor localised
filaments continues increasing towards the target or remains fixed at
$\rho_{\Psi}\approx 1.06$ cannot be determined with the present data.

###  5.2 Velocities and turbulent flow pattern

a)b) Figure 10: a) shows the filament aspect ratio and b) the filament
velocity map as deduced form CAS. Only a reduced number of trigger locations
is shown, for visibility, with the full resolution for the region below the
X-point shown to the right. The black line indicates the transition between
the different filament types. The background $\vec{E}\times\vec{B}$ direction
in the SOL is upwards for these discharges (dark green arrows).

Following the discussion about filament shapes around the X-point, we focus on
their cross-field velocities that are in particular important to evaluate
contribution to transport. Fig. 10 shows the 2D velocity maps illustrating the
qualitatively discussed filament displacement seen in fig. 8. Below the
X-point, both $\epsilon_{l}/\epsilon_{s}$ and the velocity map show a clear
separation between upstream connected and divertor localised filaments. Due to
their opposite poloidal propagation directions, complex interactions can occur
at the interface. The filament velocities are split in perpendicular and
tangential components to the flux surfaces, labelled $v_{r}$ and $v_{\theta}$
respectively, and compared between up- and downstream in fig. 11. $v_{r}$ is
radially increasing away from the separatrix in all observed regions.
Velocities typically range from $\approx$ 200 m/s at $\rho_{\Psi}=1.02$ up to
600 m/s at $\rho_{\Psi}=1.06$.

The constant radial velocity up to the LCFS at the outboard midplane indicates
that filaments are moving from the core into the SOL. This is less clear in
the region just above the X-point, where $v_{r}$ decreases to zero at the
separatrix, suggesting low levels of filamentary transport from closed to open
field lines in this region.

a)b)c) Figure 11: Radial profiles of the radial filament velocity component
a), of the radial velocity normalized to the flux expansion $v_{r}/f_{x}$ b)
and the poloidal velocity c). A separation in symbols is drawn between
$\epsilon_{l}/\epsilon_{s}\lessgtr 3$.

Despite differences in poloidal sizes in the different poloidal regions,
$v_{r}$ is largely invariant across most of the SOL. In contrast, C-Mod [20],
observed a three-fold higher $v_{r}$ above the X-point compared to the
outboard midplane. As the flux expansion $f_{x}$ increases strongly from
midplane to the X-point, $v_{r}/f_{x}$ would be constant if the filament
remains perfectly field-aligned [18]. Fig. 11b shows that this is well
satisfied, within experimental scatter in the data, for all regions around the
X-point and divertor. Significantly higher values of $v_{r}/f_{x}$ are,
however, measured at the outer midplane. This is currently not understood and
will need to be further explored.

The poloidal velocity $v_{\theta}$ (panel c) illustrates the
$\epsilon_{l}/\epsilon_{s}\lessgtr 3$ separation criteria: elongated, far-SOL
structures display a negative $v_{\theta}\,\sim\\!-500$ m/s in the divertor
leg. While this is consistent with the displacement expected from field-line
mapping (see fig. 8), it is in the opposite direction to the background
poloidal $\vec{E}\times\vec{B}$ (pointing upwards for these reversed $B$
discharges). Divertor localised filaments (green and yellow circles) show a
positive poloidal velocity, in line with the local $\vec{E}\times\vec{B}$
direction. Their $v_{\theta}$ dependence is similar to filaments just above
the X-point, decreasing from a magnitude of $\approx\,$1 km/s to near zero
around $\rho_{\Psi}\\!\approx\\!1.05$. Large poloidal velocities, up to
$\sim\\!3\,$km/s, are measured at the outboard midplane in the local
$\vec{E}\times\vec{B}$ direction for $\rho_{\Psi}\in[1.0,1.03]$, presumably
due to the steeper gradients at the midplane. This is not observed in the
other regions.

###  5.3 Single-point measurements and their ability to identify divertor-
localised filaments

So far, we discussed 2D measurements of filaments around the X-point. However,
often only single-point measurements are available. We deduce here quantities
from single-point measurements that are relevant for the subsequent flux
contribution analysis. At the same time, we explore whether the presence of
divertor filaments can be determined single-point parameters.

a)b)c)d)

Figure 12: The normalised signal trace $S$ and the auto-correlation waveform
of two trigger locations below the X-point: far-SOL with upstream-connected
filaments (a-b) and near-SOL with divertor localised filaments (c-d). The
number of events is counted over the 50 ms of GPI measurement.

Fig. 12 plots the normalised time traces of two selected pixels representative
for far-SOL elongated filaments and divertor localised filaments in the region
below the X-point (same locations as for fig. 9c and d). Elongated filaments
show stronger and fewer peaks compared to divertor localised filaments (red
crosses indicate CAS events). The auto-conditional wave-forms are shown in b)
and d). Divertor localised filaments show a near symmetric wave-form, whereas
elongated filaments show a steeper rise and longer tail, as often observed at
the outer midplane [47]. The auto-correlation time $\tau_{AC}$ is determined
from the FWHM of these auto-conditional wave-forms. The filament packing
fraction $f_{fil}$, an important quantity characterising the fraction of time
filaments occupy in a specific location, is evaluated as
$\nu_{det}\;\tau_{AC}$ [48], where $\nu_{det}$ is the filament detection
frequency. These three quantities are shown in fig. 13.

a)b)c)d) Figure 13: Filament auto-correlation time a), filament detection
frequency b) and packing fraction c) in the three different SOL regions. Panel
d) shows the ratio between the e-folding time of the increasing
($\lambda_{L}$) and decreasing ($\lambda_{R}$) part of the auto-conditionally-
averaged filament waveforms.

Fewer upstream-connected filaments, $\nu_{det}\\!\sim\\!1.5$ kHz, are detected
below the X-point compared to just above the X-point, indicating that not all
turbulent structures survive the magnetic shearing into the divertor. A higher
$\tau_{AC}$ is seen below the X-point, in agreement with propagation in the
direction of their own major axis. Divertor localised filaments have a clear
region of appearance with a 3-fold higher $\nu_{det}\\!\sim\\!$4 kHz and
shorter $\tau_{AC}$. The transition between the two states is rather sharp,
similarly as seen for the velocity in fig. 11. Low $\nu_{det}\leq 0.8$ kHz
measured in both divertor views close to the separatrix shows little
fluctuation activity, consistent with qualitative observation in sec. 5 and in
line with a quiescent region for $\rho_{\Psi}\\!\in\\![1.0,1.02]$. The packing
fraction increases smoothly radially from the separatrix in all regions with
$f_{fil}\\!\sim\\!2$-5 %, comparable to measurements in attached conditions on
ASDEX-U [6]. Based on this quantity, no distinction can be made between
connected and divertor localised filaments. The ratio of increasing and
decreasing e-folding time of the filament auto-conditional waveform, which has
been used to analyse divertor turbulence on ASDEX-U [49], increases from above
to below the X-point at $\rho_{\Psi}\approx 1.04$. However, for
$\rho_{\Psi}<1.04$ it is hard to discern a clear poloidal difference as well
as a separation between filament types in the divertor. We conclude that
single-point measurements alone can be used to determine the presence of
divertor localised filaments in the outer divertor leg, with $\nu_{det}$ and
$\tau_{AC}$ the most promising quantities.

##  6 Estimates of the role of divertor cross-field filamentary transport

Following identification and description of divertor localised filaments, it
becomes pertinent to question whether they contribute to particle and heat
flux broadening. To address this question, we express the filament-induced
radial particle flux $\Gamma_{r,fil}$ [6] as

$\Gamma_{r,fil}=f_{fil}\;n_{fil}\langle v_{r}\rangle_{fil}$ (4)

with $\langle v_{r}\rangle_{fil}$ the average radial filament velocity (shown
in fig. 11a and $n_{e,fil}$ the electron density within the filament. The
particle flux can, however, not be characterised solely by GPI, as it does not
directly measure $n_{e,fil}$ [40, 10]. Instead, the importance of the filament
radial particle transport can be characterised by the ratio of
$\Gamma_{r,fil}$ to the parallel convective transport [6], written in eq. 5.
The electron density appears in the ratio of filament density $n_{e,fil}$ to
the average density $\langle n_{e}\rangle$, which can be related to the
normalised radiance measured with GPI as follows. There is evidence that in
the SOL, $n_{e}$ and $T_{e}$ fluctuations are strongly correlated [50, 51],
such that $\frac{n_{e,fil}}{\langle n_{e}\rangle}\approx
r\frac{T_{e,fil}}{\langle T_{e}\rangle}$, with $r$ a proportionality constant.
With this approximation, eq. 3 can be solved for $n_{e,fil}/\langle
n_{e}\rangle$ and substituted into eq. 5 to obtain eq. 6.

$\displaystyle\frac{\Gamma_{r,fil}}{\Gamma_{||,conv}}$
$\displaystyle=\frac{n_{e,fil}}{\langle n_{e}\rangle}\;\frac{f_{fil}\langle
v_{r,fil}\rangle}{\langle c_{s}\rangle\langle M_{||}\rangle}$ (5)
$\displaystyle\approx\left(\frac{S}{\alpha+r\beta}+1\right)\frac{f_{fil}\langle
v_{r,fil}\rangle}{\langle c_{s}\rangle\langle M_{||}\rangle}$ (6)

$\langle M_{||}\rangle$ is the parallel Mach number and $c_{s}$ is calculated
from time-averaged RDPA and TS below and above the X-point, respectively. An
approximately constant value of $\langle M_{||}\rangle\\!\sim\\!0.1$ (towards
the target on the LFS) is measured by the RDPA across the SOL in the vicinity
of the X-point.

Several assumptions can be made on $r$. For quantitative comparisons, linear
machines [52] showed that temperature fluctuations are important in the
interpretation of high-speed camera data, especially at low $T_{e}\sim 2$-4
eV, where $\beta\sim$4$\,\gg\alpha$. At higher $T_{e}\gtrsim 10$ eV, however,
the $T_{e}$ dependence reduces significantly and $\alpha\sim\beta$ [40].
Without available $r$ measurements, we consider negligible $T_{e}$
fluctuations [6], i.e. $r\approx 0$. We note that a non-zero, but poloidally
uniform $r$, would not change the conclusions hereafter. The exponent $\alpha$
is obtained from data provided in [40], using the local average density
$\langle n_{e}\rangle$.

a)b)c)d) Figure 14: Radial profiles of ion sound speed a), the GPI deduced
quantity related to the density fluctuation amplitude b), the packing fraction
$f_{fil}$ c) and the ratio of radial filament induced particle flux and
parallel convective flux d) for the probed regions.

Fig. 14 plots the resulting profiles of the flux ratio (eq. 6) and the
contributing quantities. The ion sound speed decreases with $\rho_{\Psi}$,
tracking the average $T_{e}$ profiles. Conversely, filament related quantities
(i.e. $\langle v_{r,fil}\rangle$ shown in fig. 11a, $n_{e,fil}/\langle
n_{e}\rangle$ and $f_{fil}$ in fig. 14) increase radially across all
measurement locations. $n_{e,fil}/\langle n_{e}\rangle$ is $\approx\,$50%
larger at the midplane compared to other locations for $\rho_{\Psi}<1.05$,
consistent with the $\sigma/\mu$ data in fig. 6. The ratio of the fluxes
(panel d) increases from the near- to far-SOL by around an order of magnitude
in all regions. More importantly, however, is that the ratio is comparable in
the divertor to the outboard midplane. This data suggests that divertor
filaments (green and yellow curves) contribute in a similar manner to radial
transport as upstream filaments , and thus contribute significantly to target
profile broadening.

a)b)c)d) Figure 15: 2D measurements of electron density a) and $T_{e}$ b)
along the outer divertor leg from RDPA. Radial profiles at 4 distances
$D_{xpt}$ to the X-point (colours corresponding to lines on 2D images) are
shown in (c-d). The purple shaded area indicates the radial domain where
divertor localised filaments are observed.

Additional information on divertor profile broadening is obtained from
$\langle n_{e}\rangle$ and $\langle T_{e}\rangle$ measurements from RDPA in
the red geometry in fig. 3, as shown in fig. 15 a)-b). For further insight,
the radial profiles at four different vertical positions in panel c)-d). The
radial domain governed by divertor localised filaments for
$D_{xpt}\\!\gtrsim\\!15$ cm is represented by the shaded area. The peak values
of the profiles show little change along the divertor leg. However, a
measurable broadening on the LFS of the peak occurs in $n_{e}$ as $D_{xpt}$
increases from 5.5 cm to 20 cm, from where on no significant further
broadening is apparent. A comparable broadening is also observed in the ion
saturation current. These observations support the conclusions based on the
preceding estimate of the particle flux contribution that the mechanism
forming divertor filaments just below the X-point contribute to the
broadening.

Interestingly, the equivalent profiles of $T_{e}$ do not show this behaviour,
suggesting that energy transport behaves differently with respect to the
particle transport. It is possible that the filaments mostly contribute to
particle transport, without significant temperature variation. Measurements
were also performed in the other two geometries in fig. 3, where $D_{xpt}$ is
larger due to the vertical plasma position. Little broadening deeper in the
divertor was observed there. We mention that the broadening in $n_{e}$,
apparent in fig. 15c, could be reproduced in repeat discharges on TCV, also in
other baffle configurations, underlying the robustness of this result.

##  7 Summary and conclusion

Taking advantage of the recently installed divertor baffles on the TCV
tokamak, a new Gas Puff Imaging diagnostic can observe both the vicinity of
the X-point and, by displacing the plasma vertically, the divertor-leg region.
Images of toroidally localised HeI line emission are acquired at a 400 kHz
frame rate allowing for detailed analysis of SOL turbulence in these regions.

In this work, experimental investigations in lower single-null, attached
L-mode plasmas with reversed magnetic field (B$\times\nabla$B pointing
upwards) were performed. The plasma was positioned at three vertical heights,
separated by $\pm 14$ cm, to probe above and below the X-point, as well as
along the outer divertor leg. The results lay out a comprehensive,
experimental description of filamentary properties around the X-point and in
the outer divertor, which in particular serves as a good basis for the
validation of turbulence simulations [28]. Elongated filaments were observed
both just above the X-point and in the far-SOL in the divertor. Their shape
and motion were shown to match well with the expected behaviour based on field
line tracing of filaments measured at the outbaord midplane. The reduced
occurrence frequency of these filaments when entering the divertor indicates
that not all these far-SOL filaments reach into the divertor. In the near-SOL
($1.02\\!<\\!\rho_{\Psi}\\!<\\!1.06$) and over a large part of the outer
divertor, higher frequency divertor localised filaments, fairly circular in
shape and with diameters $\sim 15\,\rho_{s}$, were observed. Such filaments
are generated around the region of peak electron density beyond a certain
poloidal distance from the X-point, propagating radially outwards at $\sim
0.4$ km/s. We observed that their appearance is not bound to a flux surface.
Instead, the region they occupy increases radially closer to the outer target,
spanning most of the SOL. We thus found that filaments move radially outwards
at all locations, with divertor-localised filaments having similar $v_{r}$ as
those connected to the midplane. Somewhat surprisingly, $v_{r}/f_{x}$ is,
however, a factor $\gtrsim 2$ larger at the outboard midplane. Poloidal motion
is along the local E$\times$B direction, except for upstream connected
filaments in the divertor, where field-line connectivity forces them to move
in the direction opposite to E$\times$B, away from the X-point.

Statistical properties of measured SOL fluctuations showed a largely
poloidally invariant picture. An exception is at the separatrix and near-SOL
at the outboard midplane, where larger relative fluctuation levels and
skewness are observed. This, along with positive radial filament velocities,
suggests that more turbulence is entering the SOL there. The capability to
identify divertor localised filaments from single-point measurements alone has
also been explored, showing a clear distinction mostly in the occurrence
frequency and auto-correlation time.

The impact of the identified divertor-localised filaments on the radial
particle flux is estimated to be comparable to that of filaments upstream.
From in-situ, 2D Langmuir probe measurements along the outer divertor leg,
some broadening of the radial density profiles was further observed at
distances to the X-point where divertor localised filaments start to appear.
Hence, they seem to contribute noticeably to the target density and particle
flux profile shapes. No filaments were observed to move from the peak density
location into the PFR and contributing to transport there.

Further experiments are needed to understand under which conditions divertor
localised filaments appear or if upstream filaments can reach the divertor
near-SOL in some cases. The mechanism causing these divertor localised
filaments need to be further explored. Experiments are foreseen across a
larger plasma parameter space on TCV, including high-confinement regimes. The
plasma current and collisionality [18, 9] could, in particular, influence the
magnetic and $\vec{E}\times\vec{B}$ shear and disconnection of filaments
around the X-point along with the magnetic field orientation affecting the
drifts in the divertor.

## Acknowledgements

The authors thank B. Linehan for valuable discussions. Furthermore, we thank
Y. Andrebe and H. Elian for their excellent engineering work on the design of
the diagnostic. This work was supported in part by the Swiss National Science
Foundation. This work was supported in part by the US Department of Energy
under Award Numbers DE-SC0020327 and DE-SC0010529. 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.

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