Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge
A specific nonlinear regime of electron cyclotron instability is discussed aimed at explanation of complex temporal patterns of stimulated electromagnetic radiation from a mirror trap with non-equilibrium plasma typical of ECR discharge. This regime is characterized by self-modulation of a plasma cy...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge / A.G. Shalashov, S.V. Golubev, E.D. Gospodchikov, D.A. Mansfeld, M.E. Viktorov, A.V. Vodopyanov // Вопросы атомной науки и техники. — 2013. — № 1. — С. 111-113. — Бібліогр.: 7 назв. — англ. |
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Shalashov, A.G. Golubev, S.V. Gospodchikov, E.D. Mansfeld, D.A. Viktorov, M.E. Vodopyanov, A.V. 2016-11-22T10:54:51Z 2016-11-22T10:54:51Z 2013 2013 Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge / A.G. Shalashov, S.V. Golubev, E.D. Gospodchikov, D.A. Mansfeld, M.E. Viktorov, A.V. Vodopyanov // Вопросы атомной науки и техники. — 2013. — № 1. — С. 111-113. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.35.Hr, 52.72.+v https://nasplib.isofts.kiev.ua/handle/123456789/109267 A specific nonlinear regime of electron cyclotron instability is discussed aimed at explanation of complex temporal patterns of stimulated electromagnetic radiation from a mirror trap with non-equilibrium plasma typical of ECR discharge. This regime is characterized by self-modulation of a plasma cyclotron maser due to coherent interference of two counter-propagating unstable waves with degenerate frequencies. The proposed simple theoretical model allows reproducing multi-scale behavior of quasi-periodic pulses of electromagnetic radiation and precipitation of energetic electrons detected at a laboratory setup based on a mirror trap with plasma sustained by mm-wave gyrotron radiation. Обсуждается новый нелинейный режим электронно-циклотронной неустойчивости, объясняющий сложную временную динамику импульсов электромагнитного излучения сильнонеравновесной плазмы ЭЦР-разряда в прямой магнитной ловушке. Режим реализуется при самомодуляции циклотронного мазера полем биений двух встречных неустойчивых волн с вырожденными частотами. Предложенная простая теоретическая модель позволяет воспроизвести многомасштабную структуру импульсов электромагнитного излучения и высыпания энергичных электронов, зарегистрированных в лабораторном эксперименте с использованием прямой ловушки с плазмой, поддерживаемой излучением гиротрона миллимeтрового диапазона. Обговорюється новий нелінійний режим електронно-циклотронної нестійкості, що пояснює складну часову динаміку імпульсів електромагнітного випромінювання сильнонеравномірної плазми ЕЦР-розряду в прямій магнітній пастці. Режим реалізується при самомодуляціі циклотронного мазера полем биття двох зустрічних нестійких хвиль з виродженими частотами. Запропонована проста теоретична модель дозволяє відтворити багатомасштабну структуру імпульсів електромагнітного випромінювання та висипання енергійних електронів, зареєстрованих у лабораторному експерименті з використанням прямої пастки з плазмою, що підтримується випромінюванням гіротрона миллиметрового діапазону. The work has been supported by RFBR (grants 10- 02-00441, 10-02-00646) and the Presidential Council for Young Scientist Support (grant MK-3061.2012.2). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Космическая плазма Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge Генерация широкополосного электромагнитного излучения при распаде плазмы ЭЦР-разряда в прямой магнитной ловушке Генерація широкосмугового електромагнітного випромінювання при розпаді плазми ЕЦР-розряду в прямій магнітній пастці Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge |
| spellingShingle |
Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge Shalashov, A.G. Golubev, S.V. Gospodchikov, E.D. Mansfeld, D.A. Viktorov, M.E. Vodopyanov, A.V. Космическая плазма |
| title_short |
Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge |
| title_full |
Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge |
| title_fullStr |
Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge |
| title_full_unstemmed |
Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge |
| title_sort |
generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ecr discharge |
| author |
Shalashov, A.G. Golubev, S.V. Gospodchikov, E.D. Mansfeld, D.A. Viktorov, M.E. Vodopyanov, A.V. |
| author_facet |
Shalashov, A.G. Golubev, S.V. Gospodchikov, E.D. Mansfeld, D.A. Viktorov, M.E. Vodopyanov, A.V. |
| topic |
Космическая плазма |
| topic_facet |
Космическая плазма |
| publishDate |
2013 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Генерация широкополосного электромагнитного излучения при распаде плазмы ЭЦР-разряда в прямой магнитной ловушке Генерація широкосмугового електромагнітного випромінювання при розпаді плазми ЕЦР-розряду в прямій магнітній пастці |
| description |
A specific nonlinear regime of electron cyclotron instability is discussed aimed at explanation of complex temporal patterns of stimulated electromagnetic radiation from a mirror trap with non-equilibrium plasma typical of ECR discharge. This regime is characterized by self-modulation of a plasma cyclotron maser due to coherent interference of two counter-propagating unstable waves with degenerate frequencies. The proposed simple theoretical model allows reproducing multi-scale behavior of quasi-periodic pulses of electromagnetic radiation and precipitation of energetic electrons detected at a laboratory setup based on a mirror trap with plasma sustained by mm-wave gyrotron radiation.
Обсуждается новый нелинейный режим электронно-циклотронной неустойчивости, объясняющий сложную временную динамику импульсов электромагнитного излучения сильнонеравновесной плазмы ЭЦР-разряда в прямой магнитной ловушке. Режим реализуется при самомодуляции циклотронного мазера полем биений двух встречных неустойчивых волн с вырожденными частотами. Предложенная простая теоретическая модель позволяет воспроизвести многомасштабную структуру импульсов электромагнитного излучения и высыпания энергичных электронов, зарегистрированных в лабораторном эксперименте с использованием прямой ловушки с плазмой, поддерживаемой излучением гиротрона миллимeтрового диапазона.
Обговорюється новий нелінійний режим електронно-циклотронної нестійкості, що пояснює складну часову динаміку імпульсів електромагнітного випромінювання сильнонеравномірної плазми ЕЦР-розряду в прямій магнітній пастці. Режим реалізується при самомодуляціі циклотронного мазера полем биття двох зустрічних нестійких хвиль з виродженими частотами. Запропонована проста теоретична модель дозволяє відтворити багатомасштабну структуру імпульсів електромагнітного випромінювання та висипання енергійних електронів, зареєстрованих у лабораторному експерименті з використанням прямої пастки з плазмою, що підтримується випромінюванням гіротрона миллиметрового діапазону.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/109267 |
| citation_txt |
Generation of wideband electromagnetic radiation on a decay stage of a mirror-confined plasma produced by ECR discharge / A.G. Shalashov, S.V. Golubev, E.D. Gospodchikov, D.A. Mansfeld, M.E. Viktorov, A.V. Vodopyanov // Вопросы атомной науки и техники. — 2013. — № 1. — С. 111-113. — Бібліогр.: 7 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2013. №1(83) 111
GENERATION OF WIDEBAND ELECTROMAGNETIC RADIATION
ON A DECAY STAGE OF A MIRROR-CONFINED PLASMA
PRODUCED BY ECR DISCHARGE
A.G. Shalashov, S.V. Golubev, E.D. Gospodchikov, D.A. Mansfeld,
M.E. Viktorov, A.V. Vodopyanov
Institute of Applied Physics of the Russian Academy of Sciences, N. Novgorod, Russia
A specific nonlinear regime of electron cyclotron instability is discussed aimed at explanation of complex tempo-
ral patterns of stimulated electromagnetic radiation from a mirror trap with non-equilibrium plasma typical of ECR
discharge. This regime is characterized by self-modulation of a plasma cyclotron maser due to coherent interference
of two counter-propagating unstable waves with degenerate frequencies. The proposed simple theoretical model
allows reproducing multi-scale behavior of quasi-periodic pulses of electromagnetic radiation and precipitation of
energetic electrons detected at a laboratory setup based on a mirror trap with plasma sustained by mm-wave gyro-
tron radiation.
PACS: 52.35.Hr, 52.72.+v
INTRODUCTION
Laboratory setups based on mirror traps are actively
used to simulate nonlinear wave-particle interactions in
space plasmas. In particular, we reported previously that
a new regime of electron cyclotron (EC) instability has
been revealed in a compact mirror trap during the plas-
ma decay [1]. In these experiments plasma discharge with
duration of ~1 ms was sustained by 37.5 GHz / 80 kW
gyrotron under the EC resonance conditions. The ECR
heating results in an electron distribution function that
consists of two fractions, one of them being a small en-
ergetic addition to the other component which is much
cooler and denser. In the reported experiments the bulk
plasma density is about 1013 cm-3, an electron tempera-
ture is 300 eV, a hot-electron density is 5×1010 cm-3, and
an effective hot-electron temperature (primarily the
transverse energy) is 10 keV. Detailed description on
this experiment is given in the accompanying paper [2]
in this issue. Here we only mention that intense short-
pulse (5 μs) emissions of fast (10…100 keV) electrons
and synchronous bursts of electromagnetic radiation at
the fundamental cyclotron harmonic have been observed
with about 1 ms delay after the end of the microwave
pulse supporting the initial non-equilibrium plasma.
Observed bursts form rather complex temporal patterns
– the interval between single spikes in a time series may
become irregular, spikes may join in double-bursts, and
a kind of stochastic generation regime is sometimes
detected. Typical examples of such activity are shown
in Fig. 1 (top). The important feature of this data is that
different patterns were observed quite randomly for the
same experimental conditions. In the present communi-
cation we discuss a possible simple mechanism respon-
sible for such complex and random temporal behavior
of the observed burst activity.
1. TWO-LEVEL MASER MODEL
Main features of the instability were reproduced by
the model of simple two-level maser proposed in our
previous paper [3]. The joint evolution of the hot-
electron density N and the density of the electromag-
netic energy W can be qualitatively described by the
following equations
/ , /
.
/ ( ) ,
hdN dt W N h T
dW dt W hN
κ κ
γ ν γ
= − ≈⎧
⎨
= − ≈⎩
(1)
The first equation describes the rf-field-induced losses
of hot electrons with effective temperature Th, while the
second equation describes the change of the wave en-
ergy in terms of the relation between the linear instabil-
ity growth-rate γ and dissipation ν. The coefficients κ
and h determine the losses of hot particles and the aver-
aged growth-rate, respectively. The derivation of
Eqs. (1) from the quasi-linear plasma theory and com-
prehensive discussion of its application limits can be
found, e.g., in Ref. [4].
Quasi-linear interaction of hot resonant electrons
with the electromagnetic wave exponentially increasing
at the linear stage of instability reduces its transverse
energy. As a result, some fast electrons fall within a loss
cone and leave a trap. These losses reduce the instability
growth rate and, finally, restrict the increase in the elec-
tromagnetic energy density in the system. Here the dis-
sipation is governed by electron collisions with the
background plasma thus )(tν is assumed to be known
function monotonically decreasing during the plasma
decay after the gyrotron power switch-off. Decrease in
the wave energy losses provides repeated recovery of
the instability conditions and thus serves as an effective
source of free energy. This particular feature is respon-
sible for the operation of the cyclotron maser in absence
of a direct pump at the plasma decay stage.
The above model describes relatively well some es-
sential features of the measured data, but it does not
reproduce the essential features of the latest data in
which quite different patterns of the burst activity were
observed randomly for the same experimental condi-
tions [2]. This random switching between different non-
linear regimes of instability may be explained as a result
of self-modulation of a plasma cyclotron maser due to
coherent interference of two (or more) unstable waves
with degenerate frequencies resulting in spatial modula-
tion of amplification. Let us consider a simplest case of
two counter-propagating modes with complex ampli-
tudes a+ and a– such that the wave field may be repre-
sented as follows
)exp()()exp()( tiiktatiiktaE ωξωξδ −−+−∝ −+ .
112 ISSN 1562-6016. ВАНТ. 2013. №1(83)
Note that in an axisymmetric trap spatial coordinate ξ
stands most likely for the azimuthal direction. A stand-
ing wave formed by two coherent counter-propagating
modes result in modulation n~ of the hot electron den-
sity at the second spatial harmonic, such that
{ } 0~ )]2exp()(Re[)( NiktntnN ξ+= .
In turn this results in the same modulation of the
growth-rate and in the Bragg scattering that couples the
counter-propagating modes. Taking all these effects into
account, one obtains the following modification of the
basic maser equations (1):
2 2 * * *
~ ~
2 2 *
~ ~
1 1
~2 2
*1 1
~2 2
/ (| | | |)
/ (| | | |)
.
/ ( )
/ ( )
dn dt a a n a a n a a n
dn dt a a n a a n
da dt n a a n
da dt n a a n
ν
ν
+ − + − + −
+ − + −
+ + −
− − +
⎧ = − + − −
⎪
= − + −⎪
⎨
= − +⎪
⎪ = − +⎩
(2)
Here all densities are normalized over the initial density of
hot electrons 0N , time t0γτ = and dissipation rate 0/ γν are
normalized over the initial growth-rate 00 hN=γ , the wave
amplitudes are chosen such that the wave energy is scaled in
terms of initial hot-electron energy, ||||/ 22
0 −+ += aaTNW h ,
and the superscript star denotes a complex conjugate.
Particular regimes that are of interest in context of
the present paper are related to the initial conditions
.)0(,)0(,0)0(,1)0( ~
thth aaaann −−++ ====
Here initial wave amplitudes are defined by thermal
fluctuations in a hot plasma; their level in our experi-
ments may be estimated as [5]
8
0
2
2
0
2
2 10~~8/|||| −
±
<Δ><
=
NcTN
Ea
h
th
π
ωωπδ ,
where 302~ ⋅πω GHz and ωω <Δ are, correspond-
ingly, the frequency and the spectral width of the ex-
cited mode, and 10
0 102~ ⋅N cm-3. Zero initial condi-
tion for the density modulation n~ reflects the fact that
in our case the initial density fluctuations (before the
excitation of the maser) may be ignored since the modu-
lation of inversion is over-pumped by the exciting
waves during the burst formation. In this case solutions
of equations (2) conserve the phase of wave amplitudes.
Therefore, without loss of generality one can consider only
real valued initial conditions for the wave amplitudes.
Some interesting qualitative properties of maser dynamics
in this regime have been identified in our early paper [6].
2. TOWARDS EXPLANATION
OF THE EXPERIMENTAL DATA
The dynamics of the background plasma component
is very essential for the proposed model since decreas-
ing wave losses in the background plasma actually
pump the maser instability. Unfortunately, measure-
ments of the background plasma parameters have been
possible only for the steady state ECR discharge and no
reliable data are available describing the decay phase.
So we reconstruct the electron density and temperature
during the plasma decay basing on the particle and en-
ergy balance equations solved with initial conditions
corresponded to the measured parameters of the ECR
discharge. As applied to the discussed experiment, this
technique was implemented earlier in [1, 6]. In our ex-
periment the wave losses were mainly defined by the
electron-ion collisions in the background plasma, so the
loss rate is approximately equal to the effective colli-
sional rate 2/3−∝≈ eeei TNνν [7].
Example of evolution of the loss rate is shown in
Fig. 2. Maser generation typically starts at 6.0* ≈t ms,
what corresponds to the characteristic growth rate of
17
*0 s104.4)( −⋅≈= tνγ . (3)
While the instability was observed, the collisional
loss rate can be approximated as exponential decay
7 1 3 1
0 1 * 0 1( ) exp[ ( )], 5.5 10 s , 3.8 10 s .t t tν ν ν ν ν− −= − ≈ ⋅ ≈ ⋅
At time t* the electron temperature Te is about 0.1 eV
and the typical background density is Ne ~ 1011 cm-3, the
Fig. 1. Top: oscillograms of the signals from the pin diode measured precipitations of hot electrons from the trap after
the gyrotron power is switched-off. Bottom: precipitation of hot electrons (dn/dt) calculated from equations (2) for dif-
ferent ratios δa between the initial amplitudes of two competing modes. One can see quasi-periodic (left), chaotic (cen-
ter) and double-burst (right) regimes similar to those observed experimentally. Time is normalized over initial growth-
rate (γ0). Initial conditions: a+=10–2 ν1 / γ0 , a-=10–2 δa ν1 / γ0, n=1, n~=0. Plasma decay is modeled by exponent with
ν0 / γ0= 1.05, ν1 / γ0=0.0003
ISSN 1562-6016. ВАНТ. 2013. №1(83) 113
density and pressure ratios between hot and bulk plasma
fractions are Nh / Ne ~ 0.1 and NhTh / NeTe ~ 104…105.
This data agrees to the previously published results [1].
Fig. 2. Evolution of the collisional loss rate during the
plasma decay and its analytical approximation at the
instability stage. The time interval where the instability
was observed is shown in gray
Peculiar feature of the proposed model is its sensitiv-
ity to small variations of initial conditions in the pa-
rameter range typical of described experiments. In par-
ticular, essentially different temporal patterns may be
obtained for slightly different initial amplitudes of the
counter-propagating waves while all other parameters of
the system remain the same, see Fig. 1 (lower plots).
Note that a random spread in the initial wave amplitudes
is very natural due to its thermal origin. Once excited,
both modes described above compete for the same re-
sources, namely a free energy stored in hot electrons, so
one mode typically dominates over another. The re-
sulted maser dynamics show rather complex behavior
similar to what was observed in the experiment. Note
that in the theoretical plots time is normalized over the
initial growth-rate γ0 which is a free parameter here. In
order to match the experimental data one should assume
4
01 103/ −⋅≈γν what corresponds to 7
0 103.1 ⋅≈γ s-1.
This fits well to the estimate (3) obtained from the plasma
decay modeling. Note that 7
0 10~γ is in a good agree-
ment with the kinetic cyclotron instability of the extraor
dinary wave propagating quasi-perpendicular to the mag-
netic field near the fundamental cyclotron harmonic that
may be attributed to explain our experiment [1].
CONCLUSIONS
The self-modulation of the cyclotron maser may ex-
plain qualitatively the variety and randomness of the
observed data. The proposed model is very simple so it
does not require knowledge of the details such as par-
ticular type and characteristics of the unstable modes.
Matching of the model to the experimental data results
in a realistic estimation for the growth rate typical of the
extraordinary wave instability at the fundamental cyclo-
tron resonance. However, quantitative modeling re-
quires more elaborate study which accounts for the
wave traveling outside the generation region as well as
plasma inhomogeneity in the radial direction across the
magnetic trap.
The work has been supported by RFBR (grants 10-
02-00441, 10-02-00646) and the Presidential Council
for Young Scientist Support (grant MK-3061.2012.2).
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Article received 23.09.12
ГЕНЕРАЦИЯ ШИРОКОПОЛОСНОГО ЭЛЕКТРОМАГНИТНОГО ИЗЛУЧЕНИЯ ПРИ РАСПАДЕ
ПЛАЗМЫ ЭЦР-РАЗРЯДА В ПРЯМОЙ МАГНИТНОЙ ЛОВУШКЕ
А.Г. Шалашов, С.В. Голубев, Е.Д. Господчиков, Д.А. Мансфельд, М.Е. Викторов, А.В. Водопьянов
Обсуждается новый нелинейный режим электронно-циклотронной неустойчивости, объясняющий слож-
ную временную динамику импульсов электромагнитного излучения сильнонеравновесной плазмы ЭЦР-
разряда в прямой магнитной ловушке. Режим реализуется при самомодуляции циклотронного мазера полем
биений двух встречных неустойчивых волн с вырожденными частотами. Предложенная простая теоретиче-
ская модель позволяет воспроизвести многомасштабную структуру импульсов электромагнитного излуче-
ния и высыпания энергичных электронов, зарегистрированных в лабораторном эксперименте с использова-
нием прямой ловушки с плазмой, поддерживаемой излучением гиротрона миллимeтрового диапазона.
ГЕНЕРАЦІЯ ШИРОКОСМУГОВОГО ЕЛЕКТРОМАГНІТНОГО ВИПРОМІНЮВАННЯ
ПРИ РОЗПАДІ ПЛАЗМИ ЕЦР-РОЗРЯДУ В ПРЯМІЙ МАГНІТНІЙ ПАСТЦІ
А.Г. Шалашов, С.В. Голубєв, Є.Д. Господчиков, Д.А. Мансфельд, М.Є. Вікторов, А.В. Водоп’янов
Обговорюється новий нелінійний режим електронно-циклотронної нестійкості, що пояснює складну часову
динаміку імпульсів електромагнітного випромінювання сильнонеравномірної плазми ЕЦР-розряду в прямій
магнітній пастці. Режим реалізується при самомодуляціі циклотронного мазера полем биття двох зустрічних
нестійких хвиль з виродженими частотами. Запропонована проста теоретична модель дозволяє відтворити
багатомасштабну структуру імпульсів електромагнітного випромінювання та висипання енергійних
електронів, зареєстрованих у лабораторному експерименті з використанням прямої пастки з плазмою, що
підтримується випромінюванням гіротрона миллиметрового діапазону.
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