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# Radial Convection of Plasma Structures in a Turbulent Rotating Magnetized-Plasma Column

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## Abstract

The turbulent regime of a rotating magnetized plasma column has been studied. The detection and the spatiotemporal analysis of structures by means of conditional sampling techniques is performed. Because of the overall rotation and centrifugal effects, the structures inside the turbulence move on average along a spiral trajectory leading to a net radial convection of the charged particles to the walls. The development of a poloidal electric field inside the structures has been measured. It leads to the observed outwards radial E x B drift in agreement with the expectations of recent theoretical works.
Radial Convection of Plasma Structures in a Turbulent Rotating Magnetized-Plasma Column
Th. Pierre,
1
A. Escarguel,
1
D. Guyomarc’h,
1
R. Ba r n i ,
2
and C. Ricca rdi
2
1
Laboratoire PIIM, UMR 6633 CNRS, Universite
´de Provence, 13397 Marseille CEDEX 20, France
2
Universita
´di Milano-Bicocca e INFM, piazza della Scienza, 3 20126 Milano, Italy
(Received 3 July 2003; published 12 February 2004)
The turbulent regime of a rotating magnetized plasma column has been studied. The detection and
the spatiotemporal analysis of str uctures by means of conditional sa mpling techniques is performed.
Because of the overall rotation and centrifugal effects, the structures inside the turbulence move on
average along a spiral trajectory leading to a net radial convection of t he cha rged pa rticles to the walls.
The development of a poloidal electric ﬁeld inside the str uctures has been measured. It leads to the
observed outwards radial EBdrift in agreement with t he expectations of recent theoretical works.
DOI: 10.1103/PhysRevLett.92.065004 PACS numbers: 52.35.Ra, 52.25.Xz, 52.55.Dy
The turbulence induced anomalous transport mecha-
nism in magnetized plasmas is a major unsolved problem
affecting both our basic plasma physics understanding
and the performances of fusion aimed devices. In recent
years, a growing consensus is building up in pointing
towards the role of burstlike intermittent ﬂuctuations in
the transport both in tokamak scrape-off layers (SOL)
[1,2] and in other magnetized plasmas, including stella-
rators [3], simple magnetized tori [4,5], and linear Q
machines [6]. Different authors labeled such objects as
coherent vortical str uctures [4], intermittent plasma ob-
jects [1], avalanches, or avaloids [2]. The structures seem
to be convected due to electric polarization induced by
the curvature of the magnetic ﬁeld lines. These long-lived
structures are convected in the background plasma to the
walls contributing to a large extent both to particle and to
energy transpor t [1]. In a linear magnetized plasma col-
umn, the mean radial electric ﬁeld induces an EB
poloidal rotation of the column. Without drift induced
by the curvature and the gradient of the magnetic ﬁeld,
which is present only in curved devices, other mecha-
nisms should occur in order to drive a radial convection of
the structures. In linear devices, it is often assumed that
turbulence is maintained by diamagnetic drift wave in-
stability [7] or by Kelvin-Helmholtz shear ﬂow instabil-
ity [6]. However, numerous studies were devoted also to
the centrifugal effects in a rotating plasma [8] in the
decade 1970–1980. Only recently, the possible role of
the centrifugal force due to the plasma column rotation
in anomalous transport [9] was pointed out again. In our
plasma device, spiral plasma str uctures have been re-
cently observed in the regular plasma state [10], closely
resembling the form predicted by the theor y arising from
centrifugal effects [11]. Most of the papers devoted to the
centrifugal instability were motivated by the presence of
low frequency instabilities in mirror fusion devices and
pinches [12]. Recently, centrifugal effects have been used
in new conﬁnement concepts in fusion research [13].
In this Letter, we report on an experimental study of
the structures and their motion in the turbulent state of
the Mistral device. T he aim is to investigate the genera-
tion of structures in turbulence and their loss processes
across the magnetic ﬁeld. The plasma is produced by a
large multipola r source, operating a low pressure (P
15102Pa) argon discha rge in the main chamber
sustained by hot tungsten ﬁlament emission. A ﬂoating
grid separates the source from the linea r plasma column
(diameter D40 cm,Bmax 0:03 T). High energy elec-
trons injected from the source produce the magnetized
plasma column. The time averaged electron density is
longitudinally and poloidally uniform. It peaks radially
on the axis, reaching values in the range ne5108
21010cm3. The averaged electron temperature Teis
about 2 – 4 eV a nd ions stay cold (Ti0:1eV). The in-
jected negative space charge on the a xis provides the
source for a radial electric ﬁeld which makes the plasma
column rotating at the EBpoloidal velocity [10]. In
these experiments, the plasma has been conﬁned to the
linea r pa rt of the solenoid (length L1:2m)byacir-
cular collector. In order to study the different diffusion or
convection mechanisms across the magnetic ﬁeld, the
plasma column is restricted to 14 cm in diameter by a
metallic diaphragm just behind the grid at the entrance of
the column.
With the end plate globally grounded, we have ob-
served that driving the anode potential negative leads to
the onset of low frequency unstable regular waves. We
have previously reported about an m2poloidal mode
with a rotating spiral structure [10]. In the present experi-
ments (Bs0:02 T), the grid is held ﬂoating, while the
anode potential is kept negative (Va18 V). The con-
trol parameter was the potential of the collecting plate.
Transition from the m2mode ﬁrst goes through an
m1mode and then reaches a turbulent regime as the
potential of the collector is decreased from 30 to 25 and
subsequently to 20 V. Simila r transitions have been re-
ported in other devices closely resembling our setup [7].
Measurements reported below have been collected in the
turbulent regime.
Averaged and ﬂuctuating plasma pa rameters in the tur-
bulent state have been measured by means of Lang-
muir probes. Scanning of almost the whole poloidal cross
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section could be performed through an L-shaped probe
longitudinal position z100 cm from the grid. A second
radially movable probe is used as a reference and has been
inser ted at different longitudinal positions (z3050
80 cm). A time series of the electron saturation current of
the reference as well as the scanning probe have been
recorded at the same time on a digital scope with a record
length of 5104points. A time series of the ﬂoating
potential has also been measured. However, in the latter
case, in the region outside the plasma column, we ob-
served that the shape of the pulses depends strongly on the
impedance of the measurement system. Problems arising
in the measurements of the ﬂoating potential in t he pres-
ence of moderately high frequency ﬂuctuations have been
anticipated in [14]. More precisely, in ﬂoating potential
time series, we have detected long decay times a fter a
strong density pulse a rrived to the probe. This obviously
prevents a direct measurement of the electric ﬁeld inside
the plasma structures by taking the difference of two
nearby ﬂoating potential measurements, and the local
EBdrifts cannot be evaluated in such a way. We have
implemented a more accurate set of measurements by
recording the full Langmuir cha racteristic of the probes
by slowly sweeping the probe potential (40 V swept
within 10 s). Data have been analyzed in order to extract
the mean electron temperature and the mean plasma
potential.
The conditional sampling technique [15] has been used
in order to study the spatiotemporal evolution of the
structures. However, we have slightly modiﬁed the tech-
nique in order to enhance the spatiotemporal resolution.
The analysis is performed online on the electron satura-
tion current data, requiring that a pa rticula r condition is
met in the reference probe time series. A hundred time
windows of the electron saturation cur rent, about 500 s
long, have been acquired and averaged for each position
in the poloidal cross section, yielding to the reconstruc-
tion of the time evolution in the whole plasma section
using a grid of 225 positions, with a resolution of 1.5 cm.
Contrary to the standard practice [15], in which events
are selected requiring simply that the signal crosses a
ﬁxed level, we found it necessary to impose a more strin-
gent condition on the shape of the whole selected pulse.
This enhanced conditional sampling technique leads to a
sharper deﬁnition of the str uctures and to a reduced
smearing. In an effort to measure directly the electric
ﬁeld inside the structure, we have also acqui red condi-
tionally sampled time windows of the full Langmuir
characteristic by performing repeated conditional sam-
pling averages during the slow sweep of the probe poten-
tial. We have sampled only a small a rea of the poloidal
section (55cm2), to avoid stability problems of the
discharge.
Mean radial proﬁles of electron density, temperature,
and plasma potential have been obtained from averaged
Langmuir characteristics. The proﬁle of the electron den-
sity is shown in Fig. 1. The main feat ure is the presence of
an annular plateau just outside the limiter surrounding
the plasma column. The electron temperature (not dis-
played) decreases abr uptly to almost zero at the limiter.
No ionization process could happen in this region and
plasma should be continuously transported there due to
diffusive or convective ﬂows from the central column.
Mean potential proﬁles are approximately parabolic in-
side the limiter leading to an almost rigid body EB
rotation of the plasma column. The potential proﬁle ﬂat-
tens behind the limiter and the EBvelocity drops,
indicating the existence of a velocity shear behind the
limiter.
An inspection of the electron saturation current time
series recorded in the region outside the limiter shows the
appearance of intermittent pulses very large with respect
to the mean values there. On the other hand, in the internal
region, ﬂuctuations appear to be smaller (30%)and
with a more regular oscillating and quasiperiodic pattern.
No temporal delay can be detected in the time series of
two longitudinally separated probes. This is suggesting
that we are observing an almost ﬂutelike structure. The
choice of the reference probe location (r6cm,y
2cm) allows us to trigger the rise of the structures
propagating in the edge. The results of the conditional
sampling analysis, with the triggering condition de-
scribed hereupon, show a rotating spatiotemporal struc-
ture, which is displayed in Fig. 2 for a discharge operated
at a pressure of 9:2103Pa. T he time step was 2s
and the space resolution was 1.5 cm. The most striking
feature detected in the turbulence is the expulsion of a
bent tail of plasma, which we call a plasma burst, from
the cent ral column. The burst evolves along a spiral
trajectory around the column. This can be understood as
0 5 10 15 20
r (cm)
Electron Density (a.u.)
FIG. 1. Mean electron density radial proﬁle measured in the
weak turbulence reg ime. The appea rance of a circula r corona of
plasma around the plasma column is displayed.
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due to the rotation velocity decrease along the radius. The
winding up of the tail ends when the structure reaches the
walls and the plasma gets lost by recombination and
parallel collection after about 130 s. The sa me kind of
spiral structure is recorded changing the size or the shape
of the triggering pulses in the reference probe time series.
The picture appears more con fused and noisy if a tradi-
tional 2 standard deviation triggering condition is used.
As already stated, in the region of the poloidal section
inside the limiter, the electron saturation current ﬂuctua-
tions a re not much skewed and almost sym metric, with
both positive and negative pulses. However, these signa-
tures correspond to the sa me kind of structure. We have
selected events in the same discharge conditions trigger-
ing on positive pulses and negative events. The obtained
conditionally averaged time series appear to be the same
in both cases, apart from a ﬁxed time delay corresponding
almost exactly to a qua rter of the period of the plasma
column rotation. This can be understood in terms of the
eccentric rotation of the central plasma column.
The conditionally sampled events exhibit the sa me
spiral str ucture with different radial locations of the
reference probe behind the limiter. On the other hand,
the event triggered at the center of the column fails to
show a spiral tail development, thus suggesting a lack of
correlation with the edge of the column. This points out
that the structure starts developing from the edge of the
plasma column.
In order to study the plasma motion inside the struc-
ture, we need information about the local electric ﬁeld.
We have addressed such a problem performing a condi-
tional sampling of the full Langmuir characteristic of the
probe, as discussed in the previous section. The measure-
ments have been limited to a small a rea 55cm
2of the
poloidal section just across the limiter, with a resolution
of 0.5 cm. Conditionally sampled time series of electron
density, temperature, and plasma potential have been
extracted from data taken in experimental conditions
similar to the ones repor ted in Fig. 2. The results for
the electron density and the plasma potential a re dis-
played in Fig. 3 at a radial position corresponding to
the limiter. The pattern of the electron density structure
is similar to that already observed in the electron satura-
tion cur rent. Electron temperature data show that the
structure is convecting also energy in the edge of the
plasma column. A poloidal electric ﬁeld inside the struc-
ture can be inferred from the pattern of the potential.
Indeed, by comparing the time series of electron density
and plasma potential at that ﬁxed position, we ﬁnd that
the plasma potential rises as the structure arrives and
decreases afterwards. Since both the density and the
plasma potential str uctures appear to be rotating with
the whole plasma column, this means that the time varia-
tions broadly correspond to the evolution along the po-
loidal direction. Poloidal and radial components of the
instantaneous electric ﬁeld have been extracted from the
plasma potential contour plots. As a result of the str ucture
rotation, a substantial poloidal electric ﬁeld appears in-
side the structure (E35 V=m,whileEr60 V=mat
the limiter position), driving the radial convection of
plasma outside the limiter and leading to the buildup of
the spiral structure. The corresponding EBdrift ve-
locity can be calculated (vr1:7km=sat the limiter
position) and it is displayed in Fig. 4. Indeed it appea rs
to drive the plasma convection outside the limiter. We
point out that such a mechanism is likely to make a
substantial cont ribution to the total transport across the
magnetic ﬁeld lines. These results are very similar to the
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FIG. 2. Electron saturation current contour
plot obtained by enhanced conditional sa m-
pling technique. Each frame is delayed by
10 s; lines cor respond to values 1.5-2-2.5-
3-4-5-7-9 for display purpose. The develop-
ment of a spiral tail with the radial convection
of plasma to walls and its subsequent decay
during the column rotation is shown.
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conclusions of the conditional analysis of plasma str uc-
tures in the SOL of the DIII-D tokamak (see Fig. 7 in [1]).
In that case, the polarization in due to the curvature of the
B-field lines.
In conclusion, we have performed a detailed study of
the structures present in the turbulent regime of a rotating
magnetized plasma column. A conditional sa mpling
analysis shows that the bursts of plasma are propagated
radially along a spiral emanating from the plasma column
and extending outside the limiter towards the walls. The
picture strongly suggests that plasma is radially convected
inside such a structure. A simultaneous reconstruction of
both the electron density and the plasma potential time
series is achieved by conditional sampling of the full
Langmuir characteristics. For the ﬁrst time, radial con-
vection of magnetized plasma in a turbulent regime has
been experimentally proven, showing the presence inside
the structure of a poloidal electric ﬁeld inducing an E
simulations suggest that in our device centrifugal effects
[8,9] can be responsible for the observed behavior. How-
ever, more work has to be done before a direct compa rison
with the experimental data can be performed. This cen-
trifugal effect is ra rely taken into account in existing
numerical simulations of transport in fusion aimed de-
vices. However, when fast rotating plasma layers exist in
the edge of toka maks, it can be an important contribution
for the burst transport phenomenology which was re-
cently so much debated [2].
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250 275 300 325 350 375
0
1
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3
4
Electron density (a.u.)
Time
(
us
)
-9
-8
-7
-6
-5
-4
-3
Plasma potential (V)
FIG. 3. Conditionally sampled time series of electron density
(dot) and plasma potential (full) measured at the radial position
corresponding to the lim iter edge.
-10 -9 -8 -7 -6 -5
-2
-1
0
1
2
y (cm)
r (cm)
FIG. 4. Vector plot of the EBdrift velocit y extracted from
the plasma potential space distribution measured at the time
the density structure (dot) was passing by the horizontal a xis.
Limiter position is a lso shown by the dashed line. A radial drift
velocity is clearly seen inside the st ructure.
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... In the present work we present data from the toroidal Blaamann device at the Arctic University of Tromsø [1], where a discharge plasma is confined by a simple toroidal magnetic field B 0 with a possibility for adding a small vertical magnetic field. The basic physical parameters for the experiment are summarized in appendix A. Similar devices have been or are in operation elsewhere [2][3][4][5]. Some basic results concerning the performance of the Blaamann device are presented in an accompanying paper [6] (paper I), using a simplified analytical model. ...
... It was argued in paper I that the space-time variations of these two transport phenomena can be expected to be significantly different. The results presented in the following refer to one particular device, but they are relevant also for other similar experiments [2][3][4][5]. ...
... We have so far not distinguished fluctuating and steady state electrostatic potentials in (1)- (2). The coupled ion and electron dynamics in turn determine the fluctuating electric field for a given geometry [6]. ...
... A parabolic DC potential variation in Blaamann was found for several parameter sets [1,6,13,14] as also in other devices [15], except for cases with the discharge filaments placed near the wall of confining vessel. It may be worthwhile to estimate the relative importance of the rotation velocity and the bulk plasma drift induced by the plasma polarization due to the ∇B × B and curvature drifts. ...
... For typical plasma densities near the center in Blaamann we find ǫ r ≈ 3 × 10 3 . The coefficient (1 + Ω 0 /Ω ci ) on the left side of (9) accounts for a polarization due to a difference in rotation frequency for the ion and electron components found when the finite ion inertia is included [9,15,20]. The first terms on the right hand sides of (9) and (10) originate from the externally imposed potential well, so these terms are ignored for the case with E 0 = 0. ...
... Equations for ∆ x (τ ) and ∆ y (τ ) are readily found from (15). We find a limiting value for τ → ∞ as ∆ y = 2(U i + U e )ν/(θω pe ) 2 , while ∆ x increases slowly with τ . ...
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... A propos des instabilités RT et KH soulignons qu'il est possible, en particulierà grand rayon et avec un fort courant axial, d'observer dans la machine la présence de bras spiraux [Pierre04] [Barni05] qui pourraient indiquer la présence d'un flux azimutal cisaillé, et donc la possible action d'un de ces mécanismes. Cette situation a d'ailleurs donné matièreà une thèse [Brault07] où l'auteur analyse au moyen d'un diagnostic d'imagerie ultra-rapide développé au sein de l'équipe MISTRAL la structure de ces modes spiraux. ...
Thesis
La problématique du plasma en champs magnétique et électrique croisés est cruciale dans un certain nombre de situations physiques, allant de la météorologie spatiale aux procédés plus terrestres que sont la fusion par confinement magnétique ou la propulsion par effet Hall. Il est bien connu en effet que cet état est propice à l’établissement de flux de matière et d’énergie qualifiés d’anormaux puisqu’impossible a expliquer en terme de diffusion classique. On admet communément depuis plusieurs années que ce transport est intrinsèquement lié aux instabilités du milieu plasma et a la turbulence qui leur est associée. Dans notre dispositif de laboratoire a cathode chaude MISTRAL une colonne cylindrique de plasma magnétisé est produite au moyen d’un faisceau d’électrons ionisants. Dans les conditions habituelles d’expérience des instabilités à basse fréquences sont mesurées en même temps qu’un transport du plasma dans la direction transverse au champ magnétique, à l’ombre du limiteur. Le déclenchement et les caractéristiques de ces instabilités sont directement liés à la mise en place d’un champ électrique transverse étroitement conditionné par le bilan de courant. Au moyen des diagnostics (sondes, caméra intensifiée, fluorescence induite par laser) mis en œuvre nous avons pu caractériser avec beaucoup de détails la situation où un mode régulier se développe et les conditions de sa transition vers un état turbulent. L’analyse théorique menée dans ce manuscrit montre que l’influence des forces inertielles sur le fluide ionique en rotation E × B, en particulier aux forts rapports E/B obtenus sur notre dispositif, est déterminante aussi bien pour l’équilibre du plasma que sa stabilité. Il apparaît en particulier qu’à champ électrique centripète une instabilité globale analogue à celle de Simon-Hoh - puisque liée a une dérive différentielle des espèces chargées sous l’effet du freinage inertiel - est excitée. Ces résultats fournissent une explication très probable aux observations expérimentales obtenues sur notre dispositif, bien qu’une prise en compte des effets cinétiques apparaisse indispensable pour le confirmer. Mais au-delà de nos expériences, ils constituent nous l’espérons un éclairage original sur la question plus générale de la stabilité du plasma en champs croisés.
... Furthermore, recent computational studies have shown that evaluating the exact structure shapes, and the associated trajectories, could be laborious due to the large number of factors that need to be taken into account such as, magnetic geometry, collisionality, 3D effects, kinetic effects in addition to background instability and sheared flow [10][11][12]. To complement this, one could observe that turbulence studies in numerical simulations and basic plasma experiments, have greatly aided in overcoming these difficulties up to some extent with the adoption of more simplified frameworks [13][14][15][16][17][18][19][20][21]. Basic lowtemperature plasma devices, optimized for turbulence studies, enable one to perform diagnostics with sufficient spatial and temporal resolution to extract a wealth of information where equilibrium conditions can be typically achieved in a highly controllable plasma under steady-state operation. ...
Article
A steady regime dominated by intermittent blob and hole structures is identified in the plasma state of a simple magnetized torus by achieving a quasi-stationary equilibrium using an open magnetic field line configuration. The open helical field line configuration is characterized by a connection length, L_c=2a(B_φ/B_z )≳1750 cm, and pitch ratio, r_B=B_z/B_φ ≲0.01. This is realized by superposing a vertical magnetic fied, B_z, to the toroidal field, B_φ, and the regime is achieved for B_z≤0.4 mT. The combined effect of plasma rotation, arising from a substantial radial electric field, together with an open field line, results in vertically elongated plasma profiles and an asymmetric sheared poloidal flow. The analysis shows the existence of density fluctuations exhibiting universal statistical properties, dominated by non-Gaussian blob events in the edge region and holes in the core plasma, separated by a region ascribed as blob birth zone corresponding to a velocity shear layer. Two-dimensional conditional averaging analyses of fluctuations indicate that blobs form in the sheared layer, when the leading edge of an elongated coherent structure breaks off by differential stretching exerted by the background fluctuating field. Convection of this isolated blob out of the contour corresponding to the maximum radial electric field in the low field side, leads to its ejection while holes move along the same contour driven back into the main plasma. The corresponding potential structure shows counter-rotating E×B velocity field within oppositely charged structures, where the embedded electric field is consistent with the observed structure propagation. A comparison with cross-correlation analysis yields a similar conclusion except for a slight overestimation of the structure size and lifetime.
... 5 In low temperature magnetized plasmas, this happens mainly through the buildup of electrostatic potential fluctuations. 6,7 Here, we discuss the use of the multi-pin Langmuir probe, where the pins are arranged in a raster configuration in the plane perpendicular to the magnetic field lines. 8,9 Past applications had mostly focused on the measurement of the local electric field or ⃗ Ex ⃗ B particle flux. ...
Article
We discuss the measurement of the electric field drift (E→xB→ velocity) and its spatial derivatives in a low temperature magnetized plasma by means of a suitably arranged multi-pin Langmuir probe. Results are presented relating the properties of the velocity field and its electrostatic fluctuations. In particular, we have measured components of the non-linear terms in the fluid magnetohydrodynamics equation.
Article
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A noninvasive diagnostic technique relying on optical emission spectroscopy is used for studying plasma confined in a purely toroidal magnetic field. Visible emission lines of molecular hydrogen were specifically targeted. Bi-dimensional structures and poloidal plasma profiles were reconstructed from the emissivity distribution of hydrogen Fulcher system using a tomographic method. A few details concerning the methods employed to capture different emission viewlines, data reduction and tomographic reconstruction techniques are also addressed. We report also the first measurement of the excitation temperature of the $$\text {H}_2$$ H 2 [3c] level in the center of the plasma column, $$T_{\mathrm{exc}}=0.67 \pm 0.11$$ T exc = 0.67 ± 0.11 eV. Graphic Abstract
Article
In a recent paper [Phys. Plasmas 25, 061203 (2018)], the authors have presented the analysis of the electric ion drift velocity experienced by heavy ions created in a plasma submitted to a low magnetic field. Unfortunately, they have used the classical E × B drift formula that is valid only in slab geometry. The authors have not taken into account that the cylindrical geometry induces a slow electric drift of the ions around the axis of the column. Moreover, the low magnetization of the ions induces a Larmor radius that is larger than the diameter of the plasma column. The movement of the ions immediately after their creation is parallel to the local electric field, not perpendicular as indicated by the authors. Most often, the ions are neutralized before experiencing the electric drift calculated along the classical guiding center theory. This has not been taken into account carefully by the authors so that the theoretical analysis of the Laser Induced Fluorescence measurements presented in this paper is clearly invalid.
Article
The MISTRAL device is designed to produce a linear magnetized plasma column. It has been used a few years ago to study a nonlinear low frequency instability exhibiting an azimuthal number m = 2. By changing the experimental configuration of MISTRAL, this work shows experimental results on an m = 1 rotating instability with strongly different behavior. The spatio-temporal evolution of the ion velocity distribution function given by a laser-induced fluorescence diagnostic is measured to infer the radial and azimuthal velocities, ion fluxes, and electric fields. The naive image of a plasma exhibiting a global rotation is again invalidated in this m = 1 mode but in a different way. Contrary to the m = 2 mode, the rotation frequency of the instability is lower than the ion cyclotron frequency and ions exhibit a complex behavior with a radial outward flux inside the unstable arm and azimuthal ion fluxes always directed toward the unstable arm. The azimuthal ion velocity is close to zero inside the ionization region, whereas the radial ion velocity grows linearly with radius. The radial electric field is oriented inward inside the unstable arm and outward outside. An axial velocity perturbation is also present, indicating that contrary to the m = 2 mode, the m = 1 mode is not a flute mode. These results cannot be easily interpreted with existing theories.
Thesis
What do satellites thrusters, ions sources, and fusion devices have in common? They all have plasmas with orthogonal electric and magnetic fields and their size, complexity and accessibility often make them hard to be directly studied. Simpler devices, like the linear magnetised plasma device Mistral described in the manuscript, are conceived in order to understand, predict, and eventually control, some of their fundamental mechanisms. To this purpose, a tomography diagnostic is developed. Tomography is a well known diagnostic in tokamaks and stellarators, but remains seldom used in low temperature plasma experimental studies. Its main advantages are to give access to the temporal evolution of a two-dimensional section of the plasma emissivity, and to be non-intrusive. In the frame of this thesis, a tomography diagnostic has been designed from scratch, implemented, calibrated and tested. The first step consists in the adaptation of existing tomography models in this context, and the full development and validation of the associated numerical code. Then, a proof of concept is conducted with a mono-sensor diagnostic using conditional sampling on coherent rotating modes. Following, the development, configuration, and application of the full 128 channels emission tomography diagnostics on Mistral are reported. The strengths and weaknesses of this new diagnostic are presented. New insights to characterise coherent rotating modes, such as the evolution of their shape and the behaviour of the core plasma, are given. Additionally, a parametric study of the rotating modes revealed the complex and intricated effect of control parameters on the modes (existence, frequency, and mode number), and the care that has to be put in monitoring many experimental parameters.
Article
Full-text available
Low-frequency electrostatic fluctuations are studied experimentally in a low-β plasma, with particular attention to their importance for the anomalous plasma transport across magnetic field lines. The presence of large coherent structures in a turbulent background at the edge of the plasma column is demonstrated by a statistical analysis. The importance of these structures for the turbulent transport is investigated. The study is extended by a multichannel conditional analysis to illustrate detailed properties and parameter dependences of the turbulent transport
Article
Full-text available
The stability of the electron drift wave is investigated in the presence of E x B plasma rotation typical of the central cell plasma in tandem mirrors. A rotationally driven drift wave occurs at low azimuthal mode numbers. Conditions for rotational instabilities are derived. Quasilinear formulas are given for the anomalous transport associated with the unstable fluctuations.
Article
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Low‐level electrostatic ion acoustic turbulence generated by the ion–ion beam instability was investigated numerically. It is demonstrated that a conditional statistical analysis can reveal the formation, propagation, and decay of negative potential wells which correspond to ion phase‐space vortices. While the statistical analysis gives results in terms of averages over a conditionally selected subensemble, individual phase‐space structures can be investigated by small clusters of test particles placed at selected positions in phase space. The predictions of the conditional statistical analysis can be tested and their accuracy estimated by this method. A discussion of various aspects of test particle dynamics in turbulent plasmas follows naturally, with particular emphasis on conditioned particle release and relative diffusion of particles. The statistical properties of the fluctuating electric fields sampled along Lagrangian particle orbits is analyzed.
Article
Full-text available
Low‐frequency electrostatic fluctuations are studied experimentally in a low‐β plasma, with particular attention to their importance for the anomalous plasma transport across magnetic field lines. The presence of large coherent structures in a turbulent background at the edge of the plasma column is demonstrated by a statistical analysis. The importance of these structures for the turbulent transport is investigated. The study is extended by a multichannel conditional analysis to illustrate detailed properties and parameter dependences of the turbulent transport. © 1996 American Institute of Physics.
Article
Full-text available
An experimental study of low-frequency electrostatic fluctuations is presented for a plasma produced by a steady-state discharge in a magnetized toroidal plasma device without a rotational transform. A significant intermittency of the fluctuations is observed. Thus the evolution and propagation of large coherent vortical structures is demonstrated by a conditional sampling technique. The flutelike nature of the structures is explicitly demonstrated. The analysis includes measurements of fluctuations in plasma density, electric potential, and electron temperature. The relevance of the observations to anomalous transport in the device is pointed out. The performance of the conditional sampling technique is compared to a simple correlation analysis by a Monte Carlo simulation.
Article
Full-text available
Two-dimensional coherent structures in potential and saturation current have been observed in the turbulent plasma of the simple magnetized torus Blaamann, using the conditional averaging technique. The structures observed in helium plasmas are evolving in time and rotating in the poloidal cross-section with a period of about 100 μs. The time resolved average radial particle transport generated by these structures has been calculated, and it is shown that large bursty flux events occur at the vortex separatrices whenever a double vortex in the potential is formed. The time evolution of fluxes has been correlated with the dynamical evolution of the structures and their topology. The results suggest that the intermittent behaviour of the transport is due to events involving the dynamics of coherent structures on a short-timescale. The observed structures are temporally intermittent. When they occur, they cover most of the plasma cross-section.
Article
The nature of intermittency, long observed in magnetic fusion devices, was revisited lately [G. Antar et al., Phys. Rev. Lett. 87, 065001 (2001)]. It was shown that intermittency is caused by large-scale events with high radial velocity reaching about 1/10th of the sound speed. These type of structures were named “avaloids.” In the present article, the universality of convective turbulence in magnetically confined plasmas is investigated. Turbulence properties in the scrape-off layer of four different magnetic fusion devices are compared. Namely, the Tore Supra tokamak [Tore Supra Team, Nuclear Fusion, 40, 1047 (2000)] with circular cross-section limiter-bounded plasma, the Alcator C-Mod tokamak [B. LaBombard et al., Phys. Plasmas 8, 2107 (2001)] which is a divertor device, the Mega-Ampere Spherical Tokamak (MAST) [A. Sykes et al., Phys. Plasmas 8, 2101 (2001)] with vacuum chamber walls far from the plasma last closed flux surface and the PISCES linear plasma device [D. Geobel et al., Rev. Sci. Istrum. 56, 1717 (1985)]. The statistical properties of the turbulent signals in the four devices are found to be identical allowing us to conclude that intermittent convective transport by avaloids is universal in the sense that it occurs and has the same properties in many confinement devices with different configurations.
Article
The m = 1 'wobble' instability of the plasma column in a 5-m linear theta pinch has been studied using an axial array of orthogonally viewing position detectors to resolve the wavelength and frequency of the column motion. The experimental results are compared with recent theoretical predictions that include finite Larmor orbit effects. The frequency and wavelength characteristics at saturation agree with the predicted dispersion relation for a plasma rotating faster than the diamagnetic drift speed. Measurements of the magnetic fields at the ends of the pinch establish the existence of currents flowing in such a way that they short out the radial electric fields in the plasma column.
Article
The basic idea of centrifugal confinement is to use centrifugal forces from supersonic rotation to augment conventional magnetic confinement. Optimizing this “knob” results in a fusion device that features four advantages: steady state, no disruptions, superior cross-field confinement, and a simpler coil configuration. The idea rests on two prongs: first, centrifugal forces can confine plasmas to desired regions of shaped magnetic fields; second, the accompanying large velocity shear can stabilize even magnetohydrodynamic (MHD) instabilities. A third feature is that the velocity shear also viscously heats the plasma; no auxiliary heating is necessary to reach fusion temperatures. Regarding transport, the velocity shear can also quell microturbulence, leading to fully classical confinement, as there are no neoclassical effects. Classical parallel electron transport then sets the confinement time. These losses are minimized by a large Pastukhov factor resulting from the deep centrifugal potential well: at Mach 4–5, the Lawson criterion is accessible. One key issue is whether velocity shear will be sufficient by itself to stabilize MHD interchanges. Numerical simulations indicate that laminar equilibria can be obtained at Mach numbers of 4–5 but that the progression toward laminarity with increasing Mach number is accompanied by residual convection from the interchanges. The central goal of the Maryland Centrifugal Torus (MCT) [R. F. Ellis et al., Bull. Am. Phys. Soc. 44, 48 (1998)] is to obtain MHD stability from velocity shear. As an assist to accessing laminarity, MCT will incorporate two unique features: plasma elongation and toroidal magnetic field. The former raises velocity shear efficiency, and modest magnetic shear should suppress residual convection. © 2001 American Institute of Physics.