Nonlinear convective heat transport in multiple magnetized electron temperature filaments
Results are presented from a basic electron heat transport experiment consisting of multiple magnetized electron temperature filaments in close proximity. This arrangement samples cross-field transport from nonlinear drift-Alfven waves and is used to study elements of chaotic heat flow. Experiments...
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irk-123456789-1221422017-06-28T03:03:02Z Nonlinear convective heat transport in multiple magnetized electron temperature filaments Sydora, R.D. Van Compernolle Karbashewski, S. Morales, G.J. Maggs, J.E. Динамика плазмы и взаимодействие плазма-стенка Results are presented from a basic electron heat transport experiment consisting of multiple magnetized electron temperature filaments in close proximity. This arrangement samples cross-field transport from nonlinear drift-Alfven waves and is used to study elements of chaotic heat flow. Experiments are performed in the Large Plasma Device (LAPD) at the University of California. A biased LaB₆ cathode injects low energy electrons (below ionization energy) along a strong magnetic field into a pre-existing large and cold plasma forming an electron temperature filament embedded in a colder plasma, and far from the machine walls. A carbon masking plate with several holes is used to create 3 electron temperature filaments. Drift-Alfven and thermal waves from a single filament have been characterized and compared to previous studies with a different electron beam source. The 3-filament case exhibits a complex wave pattern and enhanced cross-field transport. Представлены результаты изучения переноса тепла между несколькими замагниченными нитями с электронной температурой, находящимися в непосредственной близости. Такое расположение позволяет изучать перенос тепла поперек поля из-за нелинейных дрейфово-альфвеновских волн и используется для изучения составных частей хаотического теплового потока. Эксперименты проводятся на LAPD (Large Plasma Device) в Университете Калифорнии. Смещённый LaB₆-катод инжектирует низкоэнергетичные электроны (ниже энергии ионизации) вдоль сильного магнитного поля в предварительно созданную холодную плазму больших размеров и создаёт вкраплённые нити электронной температуры вдали от стенок камеры установки. Углеродная накладка с несколькими отверстиями используется для создания трёх нитей с электронными температурами. Изучены дрейфово-альфвеновские и тепловые волны от одной нити и проведено сравнение с предыдущими результатами, полученными в другом источнике электронов. Случай с тремя нитями демонстрирует сложную волновую картину и повышенный перенос поперёк поля. Представлено результати вивчення перенесення тепла між декількома замагніченими нитками з електронною температурою, які знаходяться в безпосередній близькості. Таке розташування дозволяє вивчати перенесення тепла поперек поля через нелінійні дрейфово-альфвенівські хвилі та використовується для вивчення складових частин хаотичного теплового потоку. Експерименти проводяться на LAPD (Large Plasma Device) в Університеті Каліфорнії. Зміщений LaB₆-катод інжектує низькоенергетичні електрони (нижче енергії іонізації) уздовж сильного магнітного поля в попередньо створену холодну плазму великих розмірів і створює украплені нитки електронної температури далеко від стінок камери установки. Вуглецева накладка з декількома отворами використовується для створення трьох ниток з електронними температурами. Вивчено дрейфово-альфвенівські та теплові хвилі від однієї нитки та проведене порівняння з попередніми результатами, що отримані в іншому джерелі електронів. Випадок з трьома нитками демонструє складну хвильову картину і підвищений перенос поперек поля. 2017 Article Nonlinear convective heat transport in multiple magnetized electron temperature filaments / R.D. Sydora, B. Van Compernolle, S. Karbashewski, G.J. Morales, J.E. Maggs // Вопросы атомной науки и техники. — 2017. — № 1. — С. 100-103. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 52.25.Fi, 52.25.Gj, 52.65.Tt http://dspace.nbuv.gov.ua/handle/123456789/122142 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Динамика плазмы и взаимодействие плазма-стенка Динамика плазмы и взаимодействие плазма-стенка |
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Динамика плазмы и взаимодействие плазма-стенка Динамика плазмы и взаимодействие плазма-стенка Sydora, R.D. Van Compernolle Karbashewski, S. Morales, G.J. Maggs, J.E. Nonlinear convective heat transport in multiple magnetized electron temperature filaments Вопросы атомной науки и техники |
| description |
Results are presented from a basic electron heat transport experiment consisting of multiple magnetized electron temperature filaments in close proximity. This arrangement samples cross-field transport from nonlinear drift-Alfven waves and is used to study elements of chaotic heat flow. Experiments are performed in the Large Plasma Device (LAPD) at the University of California. A biased LaB₆ cathode injects low energy electrons (below ionization energy) along a strong magnetic field into a pre-existing large and cold plasma forming an electron temperature filament embedded in a colder plasma, and far from the machine walls. A carbon masking plate with several holes is used to create 3 electron temperature filaments. Drift-Alfven and thermal waves from a single filament have been characterized and compared to previous studies with a different electron beam source. The 3-filament case exhibits a complex wave pattern and enhanced cross-field transport. |
| format |
Article |
| author |
Sydora, R.D. Van Compernolle Karbashewski, S. Morales, G.J. Maggs, J.E. |
| author_facet |
Sydora, R.D. Van Compernolle Karbashewski, S. Morales, G.J. Maggs, J.E. |
| author_sort |
Sydora, R.D. |
| title |
Nonlinear convective heat transport in multiple magnetized electron temperature filaments |
| title_short |
Nonlinear convective heat transport in multiple magnetized electron temperature filaments |
| title_full |
Nonlinear convective heat transport in multiple magnetized electron temperature filaments |
| title_fullStr |
Nonlinear convective heat transport in multiple magnetized electron temperature filaments |
| title_full_unstemmed |
Nonlinear convective heat transport in multiple magnetized electron temperature filaments |
| title_sort |
nonlinear convective heat transport in multiple magnetized electron temperature filaments |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2017 |
| topic_facet |
Динамика плазмы и взаимодействие плазма-стенка |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/122142 |
| citation_txt |
Nonlinear convective heat transport in multiple magnetized electron temperature filaments / R.D. Sydora, B. Van Compernolle, S. Karbashewski, G.J. Morales, J.E. Maggs // Вопросы атомной науки и техники. — 2017. — № 1. — С. 100-103. — Бібліогр.: 16 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT sydorard nonlinearconvectiveheattransportinmultiplemagnetizedelectrontemperaturefilaments AT vancompernolle nonlinearconvectiveheattransportinmultiplemagnetizedelectrontemperaturefilaments AT karbashewskis nonlinearconvectiveheattransportinmultiplemagnetizedelectrontemperaturefilaments AT moralesgj nonlinearconvectiveheattransportinmultiplemagnetizedelectrontemperaturefilaments AT maggsje nonlinearconvectiveheattransportinmultiplemagnetizedelectrontemperaturefilaments |
| first_indexed |
2025-07-08T21:14:09Z |
| last_indexed |
2025-07-08T21:14:09Z |
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1837114853600264192 |
| fulltext |
PLASMA DYNAMICS AND PLASMA-WALL INTERACTION
ISSN 1562-6016. ВАНТ. 2017. №1(107)
100 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 100-103.
NONLINEAR CONVECTIVE HEAT TRANSPORT IN MULTIPLE
MAGNETIZED ELECTRON TEMPERATURE FILAMENTS
R.D. Sydora
1
, B. Van Compernolle
2
, S. Karbashewski
1
, G.J. Morales
2
, J.E. Maggs
2
1
Department of Physics, University of Alberta, Edmonton, Canada;
2
Department of Physics and Astronomy, University of California, Los Angeles, USA
Results are presented from a basic electron heat transport experiment consisting of multiple magnetized electron
temperature filaments in close proximity. This arrangement samples cross-field transport from nonlinear drift-
Alfven waves and is used to study elements of chaotic heat flow. Experiments are performed in the Large Plasma
Device (LAPD) at the University of California. A biased LaB6 cathode injects low energy electrons (below
ionization energy) along a strong magnetic field into a pre-existing large and cold plasma forming an electron
temperature filament embedded in a colder plasma, and far from the machine walls. A carbon masking plate with
several holes is used to create 3 electron temperature filaments. Drift-Alfven and thermal waves from a single
filament have been characterized and compared to previous studies with a different electron beam source. The 3-
filament case exhibits a complex wave pattern and enhanced cross-field transport.
PACS: 52.25.Fi, 52.25.Gj, 52.65.Tt
INTRODUCTION
Electron heat transport in magnetized plasmas
remains one of the active research topics within the
plasma community, primarily because of its relevance to
achieving controlled fusion. Steep cross-field pressure
gradients in magnetized plasmas can lead to the
spontaneous growth in temperature, density and
magnetic fluctuations once a certain threshold gradient
is exceeded. These fluctuations give rise to complex
heat transport processes that result in energy losses
exceeding predictions based on classical transport due
to Coulomb collisions [1-3].
To simplify the study of electron heat transport, a
series of basic experiments have been performed over
the past decade in the Large Plasma Device (LAPD) [4]
operated by the Basic Plasma Science Facility (BaPSF)
at the University of California, Los Angeles (UCLA).
Since the details of the experimental arrangement and
the major findings have been previously published [5-
11], only a brief description is given here. The generic
experiment uses a small (3 mm diameter), single-crystal
lanthanum hexaboride (LaB6) cathode to inject a low-
voltage electron beam into a strongly magnetized (1 kG),
cold, afterglow-plasma. The low-voltage beam acts as
an ideal heat source that produces a long (~8 m), narrow
(~5 mm in radius) temperature filament that is well
separated from the walls of the machine. The existence
of a transition from a regime of classical transport to
one of anomalous transport has been established
through detailed measurements. During the period of
classical transport, drift-Alfvén waves grow linearly,
driven by the temperature gradient [12].
In a macroscopic model of the temperature filament
the evolution can be described in terms of an advective-
diffusive heat equation [13]. The dimensionless number
associated with this partial differential equation is
known as the Péclet number (Pe) and is essentially the
ratio of the rate of advection by the ExB flow (VExB) to
the rate of heat diffusion( ). In the case of classical
diffusion this ratio scales like Pe=LVExB/ which for
classical heat transport becomes Pe = 0.32 ( e e)(e /Te),
Where e is the electron cyclotron frequency, e the
electron-ion collision time and is the electric potential.
In the regime where Pe > 1 convection dominates and
temperature gradients tend to be steeper. For the present
experiments the Péclet number is typically between 3
and 30 and we will be operating the filament
experiments in the higher Pe number regime so that
nonlinear convective processes associated with drift-
Alfven waves dominate.
A very recent experiment designed to study electron
heat transport, using a ring source that produces a
hollow, cylindrical heat region embedded in the
background cold plasma, has yielded some intriguing
results exhibiting intermittent collapses of the plasma
pressure profile [14]. These intermittent collapses are
interpreted as transport avalanches and are
experimentally shown to be associated with unstable
drift-Alfven waves. To create the hollow electron
temperature filament a new source was designed.
Instead of using a LaB6 crystal as in the earlier
experiments a secondary disk-shaped cathode [15] made
of LaB6 is inserted into the machine at the opposite end
of the barium oxide (BaO) coated cathode. The front
side of the LaB6 disk, which is 8 cm in diameter, is
masked by carbon plates to leave a ring of exposed
LaB6 with 4 cm inner diameter and 6cm outer diameter.
A modification of this source was used for the
generation of multiple temperature filaments as will be
explained in the next section.
In this paper we investigate electron temperature
filament-filament interactions within the context of
nonlinear convective heat transport using similar base
parameters as in the previous experiments. Previous
results from the 3 mm filament experiments using single
crystals have shown that deterministic chaos drives the
cross-field transport. In the three filament scenario we
expect chaotic transport between the three filaments will
be enhanced since the electrons are ExB convected from
one filament to the next when they are in close
proximity.
1. EXPERIMENTAL SETUP
For the first set of experiments we use the cathode
with carbon masking technique to create several
filaments. Working with the 8 cm diameter LaB6
ISSN 1562-6016. ВАНТ. 2017. №1(107) 101
secondary cathode we apply a carbon mask with 3
separate holes, each 1.0 cm diameter, and with hole
separation of 1.5 cm from center-to-center. The location
of the LaB6 secondary cathode and carbon mask is
shown in Fig. 1. The small spacing between holes is
chosen such that the cross-field spatial interaction
between the drift-Alfven waves will be enhanced, thus
modifying the transport behavior.
Emission currents of the LaB6 cathode are
approximately a few amperes and the temperature of the
cold background plasma rises from 0.25 eV to about
5 eV when a bias voltage of 10…20 V is applied. The
densities in the afterglow phase of the main discharge
are about 10
12
cm
-3
and the background magnetic field
of 1000 G was used.
a
b
Fig. 1. Schematic of the experimental setup. The main
LAPD cathode-anode operates at 1 Hz, with 15 ms
pulses. When the LAPD plasma reaches steady state, the
LaB6 cathode-anode is pulsed on. Probe access through
ball valves at multiple z locations allows for three
dimensional probing of the plasma (a); photo of the
carbon masking plate situated in front of the LaB6
cathode (b)
2. RESULTS OF MULTI-FILAMENT
EXPERIMENT
The results of Langmuir probe measurements in a
2D plane located approximately 3m from the LaB6
cathode source are shown in Fig. 2. In this figure the ion
saturation current is shown at three different times
following the source turn-on. It clearly shows the
presence of distinct filaments that begin to interact
nonlinearly within a fraction of a milli-second. In the
next set of results we examine the spatial structure of
the various low frequency fluctuations that are present.
In Fig. 3 the amplitude of the ion saturation current in
the 2D plane is shown for one of the dominant low
frequency modes (drift-Alfven) at 20.8 kHz.
a
b
c
Fig. 2. Sequence of frames at three different times
13.041 ms (a); 13.14 ms (b); and 13.219 ms (c);
depicting the Langmuir probe measurements of ion
saturation current in a 2D plane, located about 3 m
from the LaB6 cathode source
These modes are localized to the maximum thermal
gradient region in each filament and we observe that
they are only weakly spatially overlapping. The
azimuthal mode numbers of these drift-Alfven waves
ranges from m=1…3 on each filament.
102 ISSN 1562-6016. ВАНТ. 2017. №1(107)
Fig. 3. Amplitude of the ion saturation current in a 2D
plane for fixed frequency 20.8 kHz. Bias voltage of 20 V
and 1 kG magnetic field were used
a
b
Fig. 4. Frequency versus y position at fixed x location
indicated by dashed line in Fig. 3, for a)bias voltage of
10 V, and b) bias voltage of 20 V. Magnetic field of
1 kG was used
Different frequencies were examined, spatially at a
fixed x-position, along a y-cut indicated by a dotted line
in Fig. 3. As illustrated in Fig. 4,a, for bias voltage of
10 V and 1 kG magnetic field, the 20.8 kHz drift-Alfven
modes are not strongly overlapped, however, the
1…5 kHz fluctuations are more significantly interacting.
The origin of these lower frequency eigenmodes is
currently being investigated. When the bias voltage is
raised to 20 V there is an enhancement of the 1…5 kHz
range fluctuations and a modification of the amplitude
around 20 kHz. This is partially due to the enhanced
convective transport and rotation of the three filaments.
3. DRIFT-ALFVEN MODES
For determination of the temperature gradient-driven
drift-Alfven mode frequencies it is useful to first
consider a simple, local description of the drift-Alfvén
instability associated with a pure electron temperature
gradient in order to identify the parameter dependencies.
The relevant dispersion relation is given by Eq. (30) of
Ref. [12]
0)(
2
1
1 *
22
2
22
e
Az
s Z
Vk
k ,
where the local electron diamagnetic drift frequency is
with Ωe the electron gyrofrequency
, the temperature
scale length, kθ = m/r the local azimuthal wave number,
and s =cs / Ωi the ion sound gyroradius, defined as the
ratio of the ion sound speed cs
to the ion cyclotron
frequency Ωi. The local electron thermal velocity is Ve
and the Alfvén speed is VA, while Z corresponds to the
derivative, with respect to argument, of the standard
plasma dispersion function. In the dispersion relation
the terms inside the left bracket describe the zero
electron mass (MHD) shear Alfvén wave branch, while
the terms inside the right bracket describe the
collisionless, drift-wave branch. For small transverse
scales (i.e., large kθ), as is appropriate for this study, the
two branches are coupled and result in a collective
mode known as the drift-Alfvén wave, which can
become unstable for certain values of the azimuthal
mode number, m, and axial wave number kz. The
accurate calculation of the linear growth rates and real
frequencies requires the solution of coupled differential
equations for the electric and magnetic potentials to
determine the complex eigenfrequencies and the
associated eigenfunctions that satisfy the proper
boundary conditions. Such an analysis has been
performed for the temperature filaments considered here.
The range of excited azimuthal mode numbers is m~1-6,
the frequency of oscillations is Reω 0.09 Ωi, and the
higher mode-numbers show relatively fast growth
(comparable to the real frequency). The linear theory
predicts a dominant frequency of approximately 25 kHz
which is in rough agreement with the observed values.
CONCLUSIONS
In this paper results are presented from a basic
electron heat transport experiment designed to produce
multiple magnetized electron temperature filaments in
close proximity. This arrangement samples cross-field
transport from nonlinear drift-Alfven waves and is used
to study elements of chaotic heat flow. Experiments are
performed in the Large Plasma Device (LAPD) at the
ISSN 1562-6016. ВАНТ. 2017. №1(107) 103
University of California. A biased LaB6 cathode injects
low energy electrons (below ionization energy) along a
strong magnetic field into a pre-existing large and cold
plasma forming an electron temperature filament
embedded in a colder plasma, and far from the machine
walls. A carbon masking plate with several holes is used
to create 3 electron temperature filaments. Drift-Alfven
and thermal waves from a single filament have been
characterized and compared to previous studies with a
different electron beam source. The 3-filament case
exhibits a complex wave pattern and enhanced cross-
field transport. The nonlinear interaction amongst the
filaments is dominated by fluctuations in the range
1…5 kHz which is much lower than the temperature
gradient-driven drift-Alfven modes, which are in the
20…30 kHz frequency range. Characterization of the
nonlinear eigenmodes is currently underway with
guidance from a nonlinear gyrokinetic particle
simulation model [16] and results will be reported in a
separate paper.
ACKNOWLEDGEMENTS
The work of RDS and SK is supported by the
Natural Science and Engineering Research Council
(NSERC) of Canada and that of JEM, GJM and BVC is
performed under the auspices of the Basic Plasma
Science Facility (BaPSF) at UCLA which is supported
by a DOE-NSF cooperative agreement.
REFERENCES
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T.A. Carter // Phys. Rev. Lett. 2008, v. 101, p.085001.
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T.A. Carter // Phys. Plasmas. 2008, v. 15, p. 122304.
11. J.E. Maggs, G.J. Morales // Plasma Phys. Control.
Fusion. 2013, v. 55, p. 085015.
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Plasmas. 2000, v. 7, p. 144.
13. M. Shi, D.C. Pace, G.J. Morales, J.E. Maggs,
T.A. Carter // Phys. Plasmas. 2009, v. 16, p. 062306.
14. B. Van Compernolle, G.J. Morales, J.E. Maggs,
R.D. Sydora // Phys. Rev. E. 2015, v. 91, p. 031102(R).
15. B. Van Compernolle, W. Gekelman, P. Pribyl,
C. Cooper // Phys. Plasmas. 2011, v. 18, p. 123501.
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Compernolle // Phys. Plasmas. 2015, v. 22, p. 102303.
Article received 27.12.2016
НЕЛИНЕЙНЫЙ КОНВЕКТИВНЫЙ ПЕРЕНОС ТЕПЛА В НЕСКОЛЬКИХ ЗАМАГНИЧЕННЫХ
НИТЯХ С ЭЛЕКТРОННОЙ ТЕМПЕРАТУРОЙ
R.D. Sydora, B. Van Compernolle, S. Karbashewski, G.J. Morales, J.E. Maggs
Представлены результаты изучения переноса тепла между несколькими замагниченными нитями с
электронной температурой, находящимися в непосредственной близости. Такое расположение позволяет
изучать перенос тепла поперек поля из-за нелинейных дрейфово-альфвеновских волн и используется для
изучения составных частей хаотического теплового потока. Эксперименты проводятся на LAPD (Large
Plasma Device) в Университете Калифорнии. Смещённый LaB6-катод инжектирует низкоэнергетичные
электроны (ниже энергии ионизации) вдоль сильного магнитного поля в предварительно созданную
холодную плазму больших размеров и создаёт вкраплённые нити электронной температуры вдали от стенок
камеры установки. Углеродная накладка с несколькими отверстиями используется для создания трёх нитей с
электронными температурами. Изучены дрейфово-альфвеновские и тепловые волны от одной нити и
проведено сравнение с предыдущими результатами, полученными в другом источнике электронов. Случай с
тремя нитями демонстрирует сложную волновую картину и повышенный перенос поперёк поля.
НЕЛІНІЙНЕ КОНВЕКТИВНЕ ПЕРЕНЕСЕННЯ ТЕПЛА В КІЛЬКОХ ЗАМАГНІЧЕНИХ НИТКАХ
З ЕЛЕКТРОННОЮ ТЕМПЕРАТУРОЮ
R.D. Sydora, B. Van Compernolle, S. Karbashewski, G.J. Morales, J.E. Maggs
Представлено результати вивчення перенесення тепла між декількома замагніченими нитками з
електронною температурою, які знаходяться в безпосередній близькості. Таке розташування дозволяє
вивчати перенесення тепла поперек поля через нелінійні дрейфово-альфвенівські хвилі та використовується
для вивчення складових частин хаотичного теплового потоку. Експерименти проводяться на LAPD (Large
Plasma Device) в Університеті Каліфорнії. Зміщений LaB6-катод інжектує низькоенергетичні електрони
(нижче енергії іонізації) уздовж сильного магнітного поля в попередньо створену холодну плазму великих
розмірів і створює украплені нитки електронної температури далеко від стінок камери установки. Вуглецева
накладка з декількома отворами використовується для створення трьох ниток з електронними
температурами. Вивчено дрейфово-альфвенівські та теплові хвилі від однієї нитки та проведене порівняння
з попередніми результатами, що отримані в іншому джерелі електронів. Випадок з трьома нитками
демонструє складну хвильову картину і підвищений перенос поперек поля.
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