Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity
Some properties of chorus radiation while magnetosphere substorm are discussed. The influence of the hydro magnetic waves on the electron distribution function is studied by numerical simulations. A quasi-linear 2D in velocity space operator models the electron damping of plasma eigenmodes. The dyna...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2007 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
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| Cite this: | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity / V.I. Karas`, I.F. Potapenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 124-126. — Бібліогр.: 5 назв. — англ. |
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| author | Karas, V.I. Potapenko, I.F. |
| author_facet | Karas, V.I. Potapenko, I.F. |
| citation_txt | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity / V.I. Karas`, I.F. Potapenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 124-126. — Бібліогр.: 5 назв. — англ. |
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| description | Some properties of chorus radiation while magnetosphere substorm are discussed. The influence of the hydro magnetic waves on the electron distribution function is studied by numerical simulations. A quasi-linear 2D in velocity space operator models the electron damping of plasma eigenmodes. The dynamic of process is estimated under condition of varying in time of phase velocity and hence of phase resonance on the base of chorus radiation while substorms. This allows us to explain acceleration and heating of energetic electrons that double up energy during the stage of substorm.
Обговорюються деякі властивості хорового випромінювання. Чисельними методами досліджується вплив магнітогідродинамічних хвиль на функцію розподілу електронів. Квазілінійний двовимірний у просторі швидкостей оператор моделює електронне затухання плазмових власних хвиль. Динаміка процесу описана в умовах, коли змінюється за часом фазова швидкість, а, тому, і фазовий резонанс, на основі хорового випромінювання під час суббурі. Це дозволило нам пояснити прискорення і нагрів енергетичних електронів, котрі подвоюють свою енергію під час стадії суббурі.
Обсуждаются некоторые свойства хорового излучения. Численными методами исследуется влияние магнитогидродинамических волн на функцию распределения электронов. Квазилинейный двумерный в скоростном пространстве оператор моделирует электронное затухание плазменных собственных волн. Динамика процесса описана в условиях изменяющейся со временем фазовой скорости, а, следовательно, и фазового резонанса на основе хорового излучения во время суббури. Это позволило нам объяснить ускорение и нагрев энергетичных электронов, удваивающих свою энергию во время стадии суббури.
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| first_indexed | 2025-12-07T15:27:39Z |
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| fulltext |
124 Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 124-126
ELECTRON HEATING AND ACCELERATION WHILE
MAGNETOSPHERE SUBSTORM DUE TO VARYING WHISTLER WAVE
PHASE VELOCITY
V.I. Karas`, I.F. Potapenko1
NSC “Kharkov Institute of Physics andTechnology”,
Akademicheskaya Str.1, 61108, Kharkov, Ukraine;
1Keldysh Institute of Applied Mathematics of RAS,
Miusskaya Sq.4, 125047, Moscow, Russia, e-mail: firena@yandex.ru, irina@KELDYSH.ru
Some properties of chorus radiation while magnetosphere substorm are discussed. The influence of the hydro magnetic
waves on the electron distribution function is studied by numerical simulations. A quasi-linear 2D in velocity space
operator models the electron damping of plasma eigenmodes. The dynamic of process is estimated under condition of
varying in time of phase velocity and hence of phase resonance on the base of chorus radiation while substorms. This
allows us to explain acceleration and heating of energetic electrons that double up energy during the stage of substorm.
PACS: 94.30.-d
1. PRELIMINARIES
The effects of particle precipitation in the Earth’s
aurora zone are discussed in numerous publications (for
example, [1,2]). Studies have shown that the electron
precipitation related to substorms can be induced by
wave-particle interactions around the magnetospheric
equatorial plane. Those waves can be generated in the
Earth's magnetosphere due to the maser-effect [3]. A sig-
nificant number of observational data on electron precipi-
tation has been correlated to chorus [4]. In this paper we
address the following problem. We consider that the tur-
bulence is composed of hydro magnetic waves that are
assumed to be propagation along the ambient magnetic
field. The wave power absorption mechanism due to Lan-
dau damping is considered in the framework of the stan-
dard quasi-linear theory of wave-particle interaction. For
simplicity we use the local approximation in which the
velocity space is connected with the given force line of
the magnetic field. Thus the magnetized plasma is as-
sumed to be space homogeneous and that charge neutral-
ity is provided. The hydro magnetic wave level is not too
high, so the weak turbulence theory can be applied. Start-
ing with the initial Maxwellian distribution we describe
the evolution of the electron distribution function with
following equation
Here D is the standard quasi-linear coefficient
)(/
2
22 vkEmeD
k
k −∑= ωδπ which contains the
information about averaged wave amplitudes. The value
of the wave packet width is taken approximately of the
phase velocity order phph vv ~∆ . We use the following
simple approximation for D in which the diffusion coeffi-
cient is constant within the phase region and equals zero
in other parts of the velocity space: ,constD = if
phph vvv ∆≤− , and 0=D , otherwise. The inte-
grals ∫ vfdr
and ∫ vdfv r2 are defined normalized parti-
cle density and energy, respectively. The phase resonance
region and the values of the diffusion coefficient, which
are the parameters of the problem, define the electron
scattering into the loss cone, i.e. energy and the particle
flux, due to waves. Any external particle sources usually
are not taken into account and the plasma dynamics is
studied over the plasma decay. Therefore, we deal with
quasi-stationary state problem. Under the wave influence
the electron distribution function tends to the form of a
`plateau' with respect to the parallel velocity in the reso-
nance region. The anisotropy of the distribution func-
tion over pitch angles depends on time and after some
relaxation period the electron function takes on a quasi-
stationary form. The particles diffused toward high paral-
lel velocities would enter the loss cone and would escape
from the trap at once. Thus, the waves induce precipita-
tion in two ways: due to a distortion of the electron dis-
tribution over pitch angles and due to the plasma heating.
Magnetosphere is considered being Alfvén maser and
the characteristic time of the electron losses out of the
magnetic trap with the mirror ratio R is chosen equal to
10≈= RTC . Then in the above diffusion equation the
loss term is f⋅δ , where -1
CT=δ if Rvv ≥⊥/ and
,0=δ otherwise. The dynamic of the electron precipita-
tion process is estimated under the condition that the
phase velocity of the whistler waves in not constant in
time. Chorus radiation while magnetosphere substorm
(see, for example, [4]) consists in successive discrete
positively inclined elements, 0/ >dtdω , that follow con-
sequently with frequency 1-10 kHz. Micro precipitation
of electrons with energy more than 20 keV is closely con-
nected with chorus. From the observation data of chorus
.0,
,
),,(
≥∞≤≤∞−
−
∂
∂
∂
∂
=
⊥
⊥
vv
f
v
fD
vdt
tvvdf
δ
mailto:firena@yandex.ru
mailto:irina@KELDYSH.ru
125
dynamic while magnetosphere substorm we take typical
parameters of the process. The velocity is normalized on
phase velocity and the characteristic time unit is 1 sec.
2. NUMERICAL SIMULATION RESULTS
We present the results of simulations for the following
parameters. We start with the initial Maxwellian distribu-
tion and present the results of numerical simulations of
the electron distribution function and rf- enhanced energy.
We give two examples of simulation results: for the diffu-
sion coefficient D=10-2 and D=10-3. The phase resonant
region moves over parallel velocity with time following
data obtained from observation. Characteristic time period
of one pulsation is subdivided on two unequal periods:
during time period 9.01 =∆t the resonant region is
maintained stable with the phase velocity equals
5.1=phv and the width to 5.0=∆ phv . Then during
the period 1.02 =∆t corresponding to chorus precipita-
tion the resonant region it is extending until 5.2=phv .
The wave packet does not change its phase velocity
width. Such a process is successively repeated during
about 0.5-1 hour. While relatively short initial stage the
Maxwellian adopts the loss cone form, then the quasi-
stationary state is established. In the Figs. 1 and 2 the av-
eraged energy of precipitated electrons and of the elec-
trons that are trapped are shown as a function of time for
two values of the diffusion coefficient D. The established
value of precipitated electron energy does not differ much
for different diffusion coefficients. The variance can be
seen in the initial stage, see Figs. 1, 2.
Fig. 1. Time dependence of normalized averaged energy
of electrons that are precipitated into loss cone (left) and
the averaged energy of the electrons in the mirror trap for
D=0.01
Obviously the time relaxation of the system to quasi-state
is shorter for larger diffusion coefficient. The dissipated
wave power and the electron velocity can be enhanced for
the wave phase velocity that increasing in time. The
quasi-linear operator with moving phase resonant region
rakes up electrons from the domain with higher density to
the higher energetic region. That is why dissipated wave
power is larger in comparison with the case when the
phase velocity region is constant. The diffusion operator
forms the distribution function plateau within the region
of its action. Fig. 3 demonstrates the electron distribution
function in the steady state for D=0.01. It should be noted
that, to form plateau for relatively small diffusion coeffi-
cients D = 0.001-0.01 within “changing ” in time phase
resonant region there is necessary to pass over hundreds
seconds.
Explanations of field-aligned particle precipitation by
means of Landau damping with varying phase velocity in
time is able to provide sufficient increase in electron en-
ergy of chorus while substorm. This allows us to explain
acceleration and heating of energetic electrons that double
up energy on the stage of substorm. In this preliminary
study, the observational data could be interpreted in terms
of the phenomena observed in the simulations. These
simulation results can be incorporated into a more com-
plicated model of the auroral activity.
Fig. 2. Time dependence of normalized averaged energy
of electrons that are precipitated into loss cone (left) and
the averaged energy of the electrons in the mirror trap for
D=0.001
Fig. 3. The steady-state electron distribution function
for D=0.01
3. SUMMARY
The established value of precipitated electron energy
does not differ much for different diffusion coefficients.
The variance can be seen in the initial stage, see Figs.1-3.
Obviously the time relaxation of the system to quasi-state
is shorter for larger diffusion coefficient. The dissipated
wave power and the electron velocity can be enhanced for
the wave phase velocity that increasing in time. The
quasi-linear operator with moving phase resonant region
126
rakes up electrons from the domain with higher density to
the higher energetic region. That is why dissipated wave
power is larger in comparison with the case when the
phase velocity region is constant. The diffusion operator
forms the distribution function plateau within the region
of its action. Fig. 3 demonstrates the electron distribution
function in the steady state for D=0.01. It should be noted
that, to form plateau for relatively small diffusion coeffi-
cients D = 0.001-0.01 within “changing ” in time phase
resonant region there is necessary to pass over hundreds
seconds.
Explanations of field-aligned particle precipitation by
means of Landau damping with varying phase velocity in
time is able to provide sufficient increase in electron en-
ergy of chorus while substorm. This allows us to explain
acceleration and heating of energetic electrons that double
up energy on the stage of substorm. In this preliminary
study, the observational data could be interpreted in terms
of the phenomena observed in the simulations. These
simulation results can be incorporated into a more com-
plicated model of the auroral activity.
REFERENCES
1. R. G Lundin, A. Gustafsson, I. Eriksson, G. Marklund
// J. Geophys. Res. 1990, v. 95, p. 5905.
2. E. Ungstrup , A. Bahnsen, H.K. Wong, M. André and
L. Matson // J. Geophys. Res.1990, vol. 95, p. 5973.
3. V.Yu. Trakhtengerts // Eur. Space Agency Spec. Publ.
1983, v. ESA-195, p.67.
4. T.G. Rosenberg, J.C. Siren, D.L. Matthews et al. //
J. Geophys. Res. 1981, v. 86, p. 5819-5832.
5. I.F.Potapenko, C.A.Azevedo // Computer Physics
Communication. 1999, v. 121-122, p. 274-277.
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|
| id | nasplib_isofts_kiev_ua-123456789-110526 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:27:39Z |
| publishDate | 2007 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Karas, V.I. Potapenko, I.F. 2017-01-04T18:11:11Z 2017-01-04T18:11:11Z 2007 Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity / V.I. Karas`, I.F. Potapenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 124-126. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 94.30.-d https://nasplib.isofts.kiev.ua/handle/123456789/110526 Some properties of chorus radiation while magnetosphere substorm are discussed. The influence of the hydro magnetic waves on the electron distribution function is studied by numerical simulations. A quasi-linear 2D in velocity space operator models the electron damping of plasma eigenmodes. The dynamic of process is estimated under condition of varying in time of phase velocity and hence of phase resonance on the base of chorus radiation while substorms. This allows us to explain acceleration and heating of energetic electrons that double up energy during the stage of substorm. Обговорюються деякі властивості хорового випромінювання. Чисельними методами досліджується вплив магнітогідродинамічних хвиль на функцію розподілу електронів. Квазілінійний двовимірний у просторі швидкостей оператор моделює електронне затухання плазмових власних хвиль. Динаміка процесу описана в умовах, коли змінюється за часом фазова швидкість, а, тому, і фазовий резонанс, на основі хорового випромінювання під час суббурі. Це дозволило нам пояснити прискорення і нагрів енергетичних електронів, котрі подвоюють свою енергію під час стадії суббурі. Обсуждаются некоторые свойства хорового излучения. Численными методами исследуется влияние магнитогидродинамических волн на функцию распределения электронов. Квазилинейный двумерный в скоростном пространстве оператор моделирует электронное затухание плазменных собственных волн. Динамика процесса описана в условиях изменяющейся со временем фазовой скорости, а, следовательно, и фазового резонанса на основе хорового излучения во время суббури. Это позволило нам объяснить ускорение и нагрев энергетичных электронов, удваивающих свою энергию во время стадии суббури. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity Нагрів та прискорення електронів при зміні фазової швидкості вістлерів при магнітосферній суббурі Нагрев и ускорение электронов при изменении фазовой скорости вистлеров при магнитосферной суббуре Article published earlier |
| spellingShingle | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity Karas, V.I. Potapenko, I.F. Plasma electronics |
| title | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity |
| title_alt | Нагрів та прискорення електронів при зміні фазової швидкості вістлерів при магнітосферній суббурі Нагрев и ускорение электронов при изменении фазовой скорости вистлеров при магнитосферной суббуре |
| title_full | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity |
| title_fullStr | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity |
| title_full_unstemmed | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity |
| title_short | Electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity |
| title_sort | electron heating and acceleration while magnetosphere substorm due to varying whistler wave phase velocity |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110526 |
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