Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas
The production of highly charged ions is very efficient in highly ionized microwave heated plasma in an electron
 cyclotron resonance ion source (ECRIS). Recent experimental results have revealed that better production of highly
 charged ions is connected with appearance of weak ion...
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| Date: | 2006 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Cite this: | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas / A.A. Ivanov, K.S. Serebrennikov, E.A. Vostrikova, K. Wiesemann // Вопросы атомной науки и техники. — 2006. — № 5. — С. 80-85. — Бібліогр.: 21 назв. — англ. |
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| author | Ivanov, A.A. Serebrennikov, K.S. Vostrikova, E.A. Wiesemann, K. |
| author_facet | Ivanov, A.A. Serebrennikov, K.S. Vostrikova, E.A. Wiesemann, K. |
| citation_txt | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas / A.A. Ivanov, K.S. Serebrennikov, E.A. Vostrikova, K. Wiesemann // Вопросы атомной науки и техники. — 2006. — № 5. — С. 80-85. — Бібліогр.: 21 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The production of highly charged ions is very efficient in highly ionized microwave heated plasma in an electron
cyclotron resonance ion source (ECRIS). Recent experimental results have revealed that better production of highly
charged ions is connected with appearance of weak ion sound turbulence arising due to decay instability of pumping
wave in an ECRIS. In some theoretical papers different ions heating due to ion sound turbulence in an ECRIS was
studied. Under appropriate conditions due to ion sound turbulence in mixture of two different gases light ions could
be heated faster than heavy ions. Since confinement of ions will be the better the lower ion temperature, the differential
ion heating enhances losses of preferentially heated light ion component, reducing at the same time losses of
the less effectively heated heavy ions. This mechanism appears to be able to explain most of phenomena observed in
experiments with “gas mixing effect”. The present article considers the “isotope effect” in an ECRIS plasmas within
the model of ion turbulent heating.
Получение высоко зарядных ионов очень эффективно в высоко ионизированной нагретой микроволнами плазме в ионном источнике на электронном циклотронном резонансе (ИИЭЦР). Последние экспериментальные результаты показали, что лучшее получение высоко зарядных ионов связано с возникновением слабой ионно-звуковой турбулентности, возникающей благодаря распадной неустойчивости волны накачки в ИИЭЦР. В некоторых теоретических работах были изучены нагрев различных ионов за счет ионно-звуковой турбулентности в ИИЭЦР. При подходящих условиях, благодаря ионно-звуковой неустойчивости в смеси двух различных газов, легкие ионы могут быть нагреты быстрее, чем тяжелые ионы. Удержание ионов лучше при низких ионных температурах, различие в нагреве ионов усиливает потери преимущественно нагретой компоненты легких ионов, уменьшая в то же время потери менее эффективно нагреваемых тяжелых ионов. Появление этого механизма способно объяснить большинство явлений, наблюдающихся в экспериментах с «эффектом газовой смеси». Настоящая статья рассматривает «изотоп-эффект» в плазме ИИЭЦР в модели ионного турбулентного нагрева.
Одержання високо зарядних іонів дуже ефективне у високо іонізованій нагрітій мікрохвилями плазмі в
іонному джерелі на електронному циклотронному резонансі (ІДЕЦР). Останні експериментальні результати
показали, що краще отримання високо зарядних іонів пов’язане з виникненням слабкої іонно-звукової
турбулентності, яка виникає завдяки розпадній нестійкості хвилі накачки в ІДЕЦР. В деяких теоретичних
роботах були вивчені нагрів різних іонів за рахунок іонно-звукової турбулентності в ІДЕЦР. При
підходящих умовах, завдяки іонно-звуковій нестійкості у суміші двох різних газів, легкі іони можуть бути
нагріті швидше, ніж важкі іони. Утримання іонів краще при низьких іонних температурах, різниця у нагріві
іонів підсилює втрати переважно нагрітої компоненти легких іонів, зменшуючи в той же час втрати менш
ефективно нагріваємих важких іонів. Поява цього механізму здатна пояснити більшість явищ, що
спостерігаються в експериментах з «ефектом газової суміші». Ця стаття розглядає «ізотоп-ефект» у плазмі ІДЕЦР у моделі іонного турбулентного нагріву.
|
| first_indexed | 2025-12-07T17:57:43Z |
| format | Article |
| fulltext |
WEAK ION SOUND TURBULENCE AND ISOTOPE ANOMALY
IN ELECTRON CYCLOTRON RESONANCE ION SOURCE PLASMAS
A.A. Ivanov, K.S. Serebrennikov, E.A. Vostrikova
Russian Research Center “Kurchatov Institute”, Moscow, Russia
E-mail: vostr@ard.kiae.ru
K. Wiesemann
Faculty of Electrical Engineering, AEPT, Ruhr-Universitaet, D-44780 Bochum, Germany
The production of highly charged ions is very efficient in highly ionized microwave heated plasma in an electron
cyclotron resonance ion source (ECRIS). Recent experimental results have revealed that better production of highly
charged ions is connected with appearance of weak ion sound turbulence arising due to decay instability of pumping
wave in an ECRIS. In some theoretical papers different ions heating due to ion sound turbulence in an ECRIS was
studied. Under appropriate conditions due to ion sound turbulence in mixture of two different gases light ions could
be heated faster than heavy ions. Since confinement of ions will be the better the lower ion temperature, the differ-
ential ion heating enhances losses of preferentially heated light ion component, reducing at the same time losses of
the less effectively heated heavy ions. This mechanism appears to be able to explain most of phenomena observed in
experiments with “gas mixing effect”. The present article considers the “isotope effect” in an ECRIS plasmas within
the model of ion turbulent heating.
PACS: 52.35.-g
1. INTRODUCTION
The ECRIS discharge plasma is confined in an open
magnetic trap (magnetic mirror trap with magnetic
hexapole for achieving a minimum B structure and sus-
tained by a high frequency electromagnetic wave, usual-
ly injected along the magnetic field from the high field
side (Fig.1) [1]. The production of highly charged ions
in the ECRIS essentially occurs in a sequence of ioniza-
tion steps caused by electron impact. In order to make
the production efficient, it is necessary to provide elec-
trons with wide range energies due to effective rf elec-
tron heating that occurs at the condition of electron cy-
clotron resonance. Usually the physics of heating in
ECRIS systems is considered in the simple mirror (SM)
geometry without taking into account effects of mini-
mum B structure [2].
The physics of plasma heating in systems similar
to ECRIS is mainly controlled by the interaction of the
incoming (pumping) wave with the electrons, the role of
ions being more passive [2]. However for the various
regimes of ECRIS plasma transport depends strongly on
the ion temperature [3]. Therefore the ion heating is an
important process and influences strongly on the ion
source performance.
The ion temperature Z
qT of a ion species with
charge state q is determined by the ion energy balance
equation, which reads in a simplified form [4, 5]
Z
q
Z
q
Z
q
ie
Z
qee
Z
q
Z
q TnTTn
td
Tnd
ττ 2
3)(
2
3)
2
3(
/ −
−
= . (1)
On the right hand side of this equation the first term
is the power taken by the ions due to collisions with the
electron population, ( ) 1/ −ieτ is the electron-ion energy
equipartition rate for ions of the charge state q , en is
the electron density, eT − electron temperature; the sec-
ond term stands for the ion energy diffusion loss rate,
Z
qτ is the ion confinement time. Since an energy ex-
change between ions is much faster than between elec-
trons and ions all ions are expected to have the same
temperature: i
Z
q TT ≡ .
Fig.1. Scheme of an ECR ion source: 1, 2 – electromag-
netic coils, 3 – hexapole (permanent magnets),
4 – plasma cavity
The beneficial effect of mixing a lighter gas in the
plasma for the production of highly charged heavy ions
(so - called “gas-mixing effect”) was discovered fifteen
years ago (see [6] and references therein). The reasons
of this phenomenon are still under discussion. Antaya
was probably the first who supposed that in the mixture
of heavy and light ions the latter may take away the en-
ergy from the heavy ions in elastic collisions thus cool-
ing them (“ion cooling” model) [7]: by elastic collisions
the electrons heat the light ions not as effective as the
highly charged heavy ions. Elastic ion-ion collisions
equalize the various ion temperatures. The lowly
charged ions have a short life time; they are lost from
the source taking away the energy also of the heavy
ions. Thus the life time of the heavy ions is increased
and their mean charge should increase in the source.
Studying the mixture of nitrogen isotopes NN/1415 in
ECRIS 2 the authors of Ref. [8] concluded that the mod-
el of “ion cooling” is not sufficient for explanation of
the “isotope effect” observed at the same time as “gas
mixing effect” [6]. They obtained an especially simple
form for the low density case, where one gets immedi-
ately the ratio of the extraction currents for a mixture of
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.80-85.80
two isotopes characterized by their nuclear mass num-
bers A:
1
2
1
−
+
=
q
q A
Aαη . (2)
Here we have replaced the indices A by 1, 2, the A1,2
are the respective mass numbers. From (2) the current
ratio for singly charged ions is expected to be almost
equal to the gas mixture ratio α in the discharge cham-
ber, so the value of ++= 1/ηηχ q can be compared with
the value given by (2). The latter is only 1.15 for +5N ,
which is too small compared to the observed χ that is
as high as 1.5 for the mixing of nitrogen isotopes
NN/1415 .
The authors of Ref. [8] also remark that the exclusive
dependence of the ion confinement times on the square
root of the masses is not sufficient to explain the anoma-
ly. They proposed to explain the isotope anomaly via dif-
ferent ion temperatures, or more precisely with a different
mass dependent heating mechanism (predominantly for
the lighter component) caused by ion Landau damping.
The confirmation of the occurrence of this mechanism is
the observation of low-frequency noises in correlation
with the anomaly corresponding to well-known ion
sound. They suggested that due to linear Landau damping
the ion sound noises heats light ions more effectively than
heavy ones and thus could influence essentially the heavy
ions resident time in the plasma and consequently better
output of higher charged heavy ions. Therefore a small
deviation in the temperatures of various ions could result
in an essential difference in the extracted currents.
As it was mentioned above the authors of Ref. [8]
explain the “isotope effect” via the linear Landau damp-
ing of ion sound on ions that is however exponentially
low at the observed velocities of ion sound. Therefore
we proposed to consider a non-linear Landau damping
of ion sound (non-linear ion sound scattering) on ions as
a mechanism of ion heating and developed the model of
ion turbulent heating of ions having different relation of
a charge to mass [3,9,10].
It should be pointed out that peculiarities of ion tur-
bulent heating due to non-linear Landau damping of ion
sound in two-ion components plasma (plasma with two
sorts of ions) have been investigated during the latest
decade (see [11] and the references therein) for the case
of the electron current driven instability. Using the re-
sults of general theory of non-linear wave-particle inter-
action for one component plasma (plasma with one sort
of ions) [12, 13] the authors of Ref. [11] for the first
time obtained the expression of ion sound spectrum in
two component plasma taking into account self-consis-
tent modification of electron and ion distribution func-
tion. At the consideration of ion turbulent heating they
have shown that the turbulent heating rate is different
for different ions. It should be pointed out that the spe-
cific feature of the ECRIS is that we could regard the
electron distribution function as unchangeable and study
the behavior of ions separately from electrons.
The appearance of low frequency noises in accom-
panying the electron heating by electromagnetic waves
with frequencies close to the electron cyclotron frequen-
cy in plasma is a consequence of the decay instability
[15,16]. The decay of the pumping electromagnetic
wave launched along the magnetic field lines occurs in
such a way that the wave vectors of the generated elec-
trostatic waves are almost opposite to each other and the
waves propagate under the small angle θ to the direc-
tion of the magnetic field lines This is the consequence
of the conservation law for the total wave momentum
and the fact that the electrostatic wavelengths are much
shorter than those of the electromagnetic pumping
wave. The condition of decay is
sh ωω +=Ω , .hs kkk
+= (3)
Here ceω≤Ω is the pumping wave frequency, which
must be close to the local electron cyclotron frequency
ceω ; )sin1( 2
22
2
θ
ωω
ω
ωω
cepe
pe
ceh
−
−= is the hybrid fre-
quency, peω is the electron plasma frequency, and sω
the ion sound frequency, the latter being much lower
than ceω .The condition of the decay (3) can be satisfied
only for a wave vector hk
directed almost parallel to
magnetic field, since the hybrid frequency is close to the
electron cyclotron frequency only in this case. Thus
θsin is very small.
The value of minimum unstable external electric
field minE in one component plasma was obtained in
the paper [17] where for the first time the parametric ex-
citation of potential waves in a completely ionized plas-
ma near electron cyclotron resonance by high frequency
electric field was studied. The author of Ref. [15,16]
shown that this process is equivalent to the two potential
wave non-linear decay of pumping wave. The maximum
growth rate of the decay instability dγ corresponds to a
frequency shift sh ωω =−Ω=∆ and is given by
[15,16,17]
ee
pe
cesd Tn
E
π
ω
ωωγ
422
1 2
2
2
⋅
Ω
⋅= , (4)
the angle θ is limited to the range
.
2
1sin0
22
cepe
cepe
ωω
ωω
θ
−
⋅<≤ (5)
It means that the electrostatic waves are unstable inside
a small cone around the direction of the magnetic field
lines with 6/, 00 πθθθ =< . This non-linear interac-
tion of three waves namely the pumping electromagnet-
ic wave, the hybrid wave and an ion sound wave broad-
ens the wave spectra and randomizes the phases of the
waves [16].
According to the paper [17] it’s possible to get the
minimum threshold of decay instability for the case of
multi components plasma at the condition 1cos ≈θ ,
pis ωω = :
eeTn
E
π4
2
min ,
2
24 2
2
Ω
Ω= ei
pepe
pi νπ
ωω
ω
(6)
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.80-85.81
Here eiν is the electron–ion collision frequency, piω is
the ion plasma frequency. It can be seen that the thresh-
old appears to be rather small for standard experimental
parameters of ECR both in one component plasma [15]
and two component plasma [18].
The form of ion sound turbulence spectrum was first
given by Kadomtsev and Petviashvili [14] for the case
of a current driven instability and studied by Tsitovich
for the case when weak ion sound turbulence is driven
by the high frequency electromagnetic wave [13]. In
both cases the results are similar: the ion sound spec-
trum expands to waves with very long wavelengths, the
steady state is provided by non-linear scattering of the
ion sound wave towards small frequencies.
Using the results of the papers [11,12,13,14] we got
the expression for ion sound spectrum for one and two
components ECRIS plasmas [3,9,10]. According to Ref.
[13] we had to consider two regions in k − space: the
first is the region of generation, where the growth of ion
sound waves is balanced by nonlinear Landau damping
and the second one, the region of inertia, where energy
flow into the lower ion sound frequencies is balanced by
linear Landau damping on electrons (Fig.2).
Fig.2. Schematic shape of ion sound spectrum: I – re-
gion of generation, II – region of inertia, III – region of
adsorption
The density of ion sound energy is given by a classi-
cal form [13]
( )
( )
( )
.
2
)(
4)(
1
2
3
2
)(
2
3
π
ω
πω
ωεω
ωπ ωω
kdkN
kd
E
k
kdWW
k
k
k
k
∫
∫∫
=
=
∂
∂==
= (7)
Here )(ωε is the plasma permittivity. The dimension
of the spectral energy kW coincides with the dimension
of energy. According to Planck the number of waves
could be introduced as )(/ kWN kk
ω= , where the
Planck constant is set equal 1. Thus the product of
)(kN k
ω has the dimension of energy and the number of
waves is not dimensionless anymore. Usually the num-
ber of waves depends on the absolute value of the wave
vector k and of the angle θ , i.e. kN = )(cosθkN
[11,12,13,14]. Since the growth rate has its maximum
close to the small angle 0θ we follow the idea of
Kadomtsev and Petviashvili [14] and express the angu-
lar dependence of the ion sound spectrum by
)cos(cos)(cos 0θθδθ −= kk NN , (8)
It turned out that the ion sound spectrum in k −
space has a saw-tooth form and depends considerably
on microwave generator power and the characteristic
parameter of the magnetic field lines (Fig.3).
Ws
k
k0n kgn k0 kg
k
Fig.3. Shape of ion sound spectrum for the case
gg kkk < <− 0
The appearance of additional areas of ion sound genera-
tion in k − space could be explained as follows: the
phases of the ion sound waves are randomized in the
area between 1−≈ Deg rk and 0k . Here 0k corresponds to
the case then 0=kN , Der − thermal electron Debye
length. Therefore the growth rate here will be much less
than the growth rate for fixed phases. In the region
0kk < ion sound noise develops. The situation here cor-
responds to the decay instability with fixed phases,
where the growth rate is determined by (4) with
)( 0ss kωω = . Thus additional stages of the instability
starts from new 0kkgn ≤ and will cause a spectral broad-
ening from gngn kk ∆+ up to nk0 . It should be pointed
out that in the area of long wave lengths where the rate of
ion sound damping on electrons ( lγ ) becomes smaller
than the ion sound damping due to ion-ion collision ( iγ )
the spectrum is cut off due to efficient ion sound absorp-
tion by ion-ion collisions. The ion sound damping due to
ion-ion collisions turns out different for one component
and two component plasma [19,20].
From the collisionless part of quasilinear equation for
the ion distribution function which includes the induced
(non-linear) scattering of ion sound waves on different
ions we obtained the equations of ion turbulent heating.
It should be pointed out that the same technique was ap-
plied to investigate the ion turbulent heating both in
case then ion sound turbulence was driven by current in-
stability [11] and in case of ion-sound kinetic parametric
instability in helicon plasma source [21]. The simple
calculation shown that under appropriate conditions due
to ion sound turbulence in mixture of two different gas-
es light ions could be heated faster than heavy ions
[3,9,10]. Since confinement of ions will be the better the
lower ion temperature, the differential ion heating en-
hances losses of preferentially heated light ion compo-
nent, reducing at the same time losses of the less effec-
tively heated heavy ions. This mechanism appears to be
able to explain most of phenomena observed in experi-
ments with “gas mixing effect”. In this paper we calcu-
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.81-86.
82
lated the probability of induced ion sound scattering on
ions for isotope case. Further we’ll study the ion turbu-
lent heating for isotope case as for mixture of two dif-
ferent gases.
2. INDUCED ION SOUND SCATTERING ON
IONS IN TWO COMPONENTS PLASMA
2.1. THE CASE OF GAS MIXTURE
As discussed before we describe ECRIS plasma in a
gas mixture as a two-ion-components plasma, i.e. plas-
ma with two sorts of ions α and β considerably. Then
the ion sound frequency sω will be expressed via the
ion plasma frequencies of both ions αω pi and βω pi
( )
.
,,
11
2
122
2
1
22
22
e
pipipi
De
pipi
s
nnqnq
rk
=+
+=
+
+
=
ββαα
βα
βα ωωω
ωω
ω
(9)
Here αn and βn denote the densities of ions of kind
α and β , respectively. The dispersion properties of
plasma as well as non-linear plasma processes are deter-
mined by the thermal electrons in the bulk of the plas-
ma.
The kinetic equation describing the induced scattering
of ion sound waves on ions is given as
11 1111
kdvNNkdvNN
t
N
kkkkkkkk
k
βα ∫∫
+ ∞
∞−
+ ∞
∞−
+=
∂
∂
.(10)
where
( )
.
2
)(),( 6
3
11, 1 π
α
αα
pdkk
p
fkkwv pkk
−⋅
∂
∂
= ∫
(11)
Here )( pf
α is distribution function of ions of sort α
supposed to be Maxwellian, ),( 1kkwp
α is the probabil-
ity of induced ion sound scattering on ions [11]
( ) ( )
( )
,
)(
2))()()((4
),(
2
)()(
2
9
11
1
1
1
1
α
ωωωω
α
ω
ε
ω
ε
ω
πωωδ
kk
k
l
k
k
l
k
p
k
vkkkk
kkw
Λ
∂
∂
∂
∂
⋅−−−
=
=
==
(12)
( )
..
)(
2
)(2
1
1
1 1
1
1
3
2
−
+
⋅⋅
=Λ
−
−
l
kk
i
kk
kk
M
q
M
q
k
vk
M
q
kk
kk
k
qe
ε
δ ε
ωωπ
β
β
β
α
α
α
αα
α
Here α1kk
Λ is the amplitude of induced ion sound scat-
tering on ions, i
kk βδ ε
1− is the contribution of ions of sort
β in plasma permitivity. Replacing index α for β in
the expressions (11), (12) one can get βkkv . After some
calculations we find that
[ ]
×
−
′′
+
+′′′
⋅
=
β
β
α
α
α
α
αα
αα
α
α
α
π ω
ωωω
ωδω
πω
M
q
M
q
M
qekv
kkv
M
q
kk
kkev
pi
Tpi
Tpi
pi
kk
4
2
22
2
1
22
2
22
1
1
4
2
4
)(
,)(1
1
.
)(
4
)(
2)(Re
2
2
2
2
2
2
1
1
4
2
1
1
2
2
1
1
1
1
1
1
×
−′′′′′
⋅+
+
−′′′
⋅
×
−
−
−
−
kk
i
kk
D
T
pi
l
kk
i
kk
r
v
M
q
M
qk
kk
kkk
k
k
k
kk
kk
kk
ε
δ ε
ωδ
π ω
ω
ωδ
ε
δ ε
β
α
α
β
β
α
α
β
(13)
Here ,1kkk
−=′′ 1kk ≈ , )()( 1kk
ωωω −=′′ , βα TT vv ,
are the thermal ions velocities, αDr is the Debye length
of ions of kind α . Neglecting the second term in the
formula (13) finally we can get
[ ]
( ) .)(
4
)()(
,)(
222
22222
2
2
1
1
4
2
1
22
2
2
22
2
2
2
1
2
1
1
4
2
111
βα
ββαα
β
β
α
α
ββ
β
β
αα
α
α
βα
ωδ
π ω
ωω
ωω
ωδ
π ω
DD
DTDT
pi
TpiTpi
pi
kkkkkk
rr
rvrv
M
q
M
q
k
kk
kkekk
v
M
q
v
M
q
kk
kk
kkevvv
+
+
−′′′′′
⋅
+
+
+
×′′′
⋅
=+=
(14)
If the density of light ions β is less than the density
of heavy ions α then under the following condition
2222
ββαα ωω TpiTpi vv > ,
2
2
2
22
1
β
α
αβα
αβ
ω
ω
pi
pi
D
De
r
r
Aq
Aq
> >
− (15)
taking into account (14) finally we can write the kinetic
equation (10) as follows:
( ) .
)(
4
)()(
1222
22222
2
2
1
1
4
2
1
1
kd
rr
rvrv
M
q
M
q
k
kk
kkekkNN
t
N
DD
DTDT
pi
kk
k
βα
ββαα
β
β
α
α
ωδ
π ω
ωω
+
+
−
×′′′′′
⋅
=
∂
∂
∫
(16)
According to a general lemma of the non-linear plas-
ma theory [13] one can get the spectrum of low frequen-
cy noises from the ion sound energy balance equation.
In the region of generation this equation is as follows:
( ) .)(
4
)()(2
1222
22222
2
2
1
1
4
2
1
1
kd
rr
rvrv
M
q
M
qk
kk
kkekkNNN
t
N
DD
DTDT
pi
kkkk
k
βα
ββαα
β
β
α
αωδ
π ω
ωω
+
+
−′′′′′
×
⋅+Γ=
∂
∂
∫
(17)
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.80-85.83
Assuming in the region of generation a stationary state
of the spectrum we get from equation (17) [3,9,10]
( )
.
)(~
62222
22222
2
4
g
gg
DTDαT
DDgpi
k
k
kkk
rvrv
rr
A
q
A
q
M
eN
−∆+
+
+
−
=
−−
β
βα
β
β
α
α
βα
ξ
γω
(18)
Here
++−=
15
2)(cos
5
1)(cos
3
1
0
2
30
2
22 θθξ PP ,
)(cosθnP are Legendre polynomials; M is proton
mass, )cos,(~~
0θγγγ gddgk kGG ===Γ , LdG /1= ,
1d is the extension of the region where decay instability
occurs, L is the length of the magnetic trap.
The spectrum in the inertial region is given as [3,9,10]
( )
.ln
~
1
8
0
2222
222
22
2
6
4
k
k
rvrv
rr
A
q
A
q
M
er
k
N
DβTDαT
DD
pe
Depi
k
β
+
+
×
×
−
=
−−
α
βα
β
β
α
α
ξω
ωπ
(19)
Here
0cos8 θ
ω
ω
ωπγ s
pe
pi
lk ==Γ , 022 cos~ θξξ = .
Matching the expressions of spectrum in these two
regions at gkk = ( gk is the point in k -space where
generation of ion sound occurs) we can find the relation
between gk and the unknown parameter 0k
g
k
pi
pe
g
g
gs
dg
kk
k
k
G
k
k ∆
≡
∆
=
ω
ω
ω
γ
π )(
~8ln
0
. (20)
2.2. THE ISOTOPE CASE
It should be pointed out that the condition (15) is not
observed for isotope case. Thus the case of isotope
should be studied separately because all terms in the ex-
pression (14) should be taken into account.
Actually for the case of two isotopes we can rewrite
the condition (15) as follows:
+
+
> >
∆
2
1
2
2
1
2
1
21
2 1
T
T
T
T
T
T
T
T
A
A
e
η
η
η . (21)
Here subscripts 1 and 2 denote first and second isotopes
responsibly,
1
2
n
n=η , ., 211 AAAAA ∆=−≡
In most cases the temperatures of isotopes are al-
most equal to each other, i.e. 21 TTTi == . Then the sat-
isfaction of the condition (21) is determined by the val-
ue of small parameter
e
i
T
T
and the value of η . It is seen
that for all isotopes the contrary condition is valid
2
2
1
2
2
1
2
1
21
∆>
+
+
A
A
T
T
T
T
T
T
T
T
e
η
η
η
. (22)
To find the probability of induced ion sound scatter-
ing on ions for isotope case one should take into account
the smallness
2
∆
A
A in the second term of (14). Thus
expanding expression (14) by the smallness
∆
A
A
we
can get the kinetic equation (10) for isotope case.
[ ] ( )
( ) .)(
)()1(16
)(
)(
)1(4
)(
12
1
2
2
12
1
2
2
1
2
21
2
11
2
2
2
2
1
12
1
2
2
12
122
11
2
21
1
1
⋅−
∆
++
++
+⋅′′′×
+
+=
∂
∂
∫
∫
kd
kk
kkkkkN
M
M
TTMn
TT
kd
kk
kkkkN
Mn
TTN
t
N
k
kk
k
ω
ηηπ
ηη
ωδ
ηπ
η
(23)
CONCLUSIONS
From the collisionless part of quasilinear equation
for the ion distribution function using the expressions of
ion sound spectrum and the probability of induced ion
sound scattering obtained from equation (23) as for gas
mixture case (see part 2.1) one could get the difference
in the rates of isotope heating. It should be pointed out
that as it was shown in Ref. [8] even a small difference
between isotope temperature (in order of 3%) could pro-
vide the increase of light isotope extraction current and
consequently better confinement of heavy ions in an
ECRIS plasmas.
This work was supported by INTAS-01-0373, IN-
TAS 97.0094, Federal Program “Integration”,
(№Я0068/2137) and scientific and technical program
“Education industry” (№ 1535).
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___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.81-86.
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СЛАБАЯ ИОННО-ЗВУКОВАЯ ТУРБУЛЕНТНОСТЬ И АНОМАЛИИ ИЗОТОПОВ В ПЛАЗМЕН-
НОМ ИОННОМ ИСТОЧНИКЕ НА ЭЛЕКТРОННОМ ЦИКЛОТРОННОМ РЕЗОНАНСЕ
A.A. Иванов, K.С. Серебренников, E.A. Вострикова, K. Виземан
Получение высоко зарядных ионов очень эффективно в высоко ионизированной нагретой микроволнами
плазме в ионном источнике на электронном циклотронном резонансе (ИИЭЦР). Последние эксперименталь-
ные результаты показали, что лучшее получение высоко зарядных ионов связано с возникновением слабой
ионно-звуковой турбулентности, возникающей благодаря распадной неустойчивости волны накачки в
ИИЭЦР. В некоторых теоретических работах были изучены нагрев различных ионов за счет ионно-звуковой
турбулентности в ИИЭЦР. При подходящих условиях, благодаря ионно-звуковой неустойчивости в смеси
двух различных газов, легкие ионы могут быть нагреты быстрее, чем тяжелые ионы. Удержание ионов луч-
ше при низких ионных температурах, различие в нагреве ионов усиливает потери преимущественно нагре-
той компоненты легких ионов, уменьшая в то же время потери менее эффективно нагреваемых тяжелых
ионов. Появление этого механизма способно объяснить большинство явлений, наблюдающихся в экспери-
ментах с «эффектом газовой смеси». Настоящая статья рассматривает «изотоп-эффект» в плазме ИИЭЦР в
модели ионного турбулентного нагрева.
СЛАБКА ІОННО-ЗВУКОВА ТУРБУЛЕНТНІСТЬ ТА АНОМАЛІЇ ІЗОТОПІВ У ПЛАЗМОВОМУ
ІОННОМУ ДЖЕРЕЛІ НА ЕЛЕКТРОННОМУ ЦИКЛОТРОННОМУ РЕЗОНАНСІ
A.A. Іванов, K.С. Серебренников, О.О. Вострикова, K. Віземан
Одержання високо зарядних іонів дуже ефективне у високо іонізованій нагрітій мікрохвилями плазмі в
іонному джерелі на електронному циклотронному резонансі (ІДЕЦР). Останні експериментальні результати
показали, що краще отримання високо зарядних іонів пов’язане з виникненням слабкої іонно-звукової
турбулентності, яка виникає завдяки розпадній нестійкості хвилі накачки в ІДЕЦР. В деяких теоретичних
роботах були вивчені нагрів різних іонів за рахунок іонно-звукової турбулентності в ІДЕЦР. При
підходящих умовах, завдяки іонно-звуковій нестійкості у суміші двох різних газів, легкі іони можуть бути
нагріті швидше, ніж важкі іони. Утримання іонів краще при низьких іонних температурах, різниця у нагріві
іонів підсилює втрати переважно нагрітої компоненти легких іонів, зменшуючи в той же час втрати менш
ефективно нагріваємих важких іонів. Поява цього механізму здатна пояснити більшість явищ, що
спостерігаються в експериментах з «ефектом газової суміші». Ця стаття розглядає «ізотоп-ефект» у плазмі
_______________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.80-85.85
ІДЕЦР у моделі іонного турбулентного нагріву.
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.81-86.
86
|
| id | nasplib_isofts_kiev_ua-123456789-81159 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:57:43Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Ivanov, A.A. Serebrennikov, K.S. Vostrikova, E.A. Wiesemann, K. 2015-05-11T19:22:35Z 2015-05-11T19:22:35Z 2006 Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas / A.A. Ivanov, K.S. Serebrennikov, E.A. Vostrikova, K. Wiesemann // Вопросы атомной науки и техники. — 2006. — № 5. — С. 80-85. — Бібліогр.: 21 назв. — англ. 1562-6016 PACS: 52.35.-g https://nasplib.isofts.kiev.ua/handle/123456789/81159 The production of highly charged ions is very efficient in highly ionized microwave heated plasma in an electron
 cyclotron resonance ion source (ECRIS). Recent experimental results have revealed that better production of highly
 charged ions is connected with appearance of weak ion sound turbulence arising due to decay instability of pumping
 wave in an ECRIS. In some theoretical papers different ions heating due to ion sound turbulence in an ECRIS was
 studied. Under appropriate conditions due to ion sound turbulence in mixture of two different gases light ions could
 be heated faster than heavy ions. Since confinement of ions will be the better the lower ion temperature, the differential
 ion heating enhances losses of preferentially heated light ion component, reducing at the same time losses of
 the less effectively heated heavy ions. This mechanism appears to be able to explain most of phenomena observed in
 experiments with “gas mixing effect”. The present article considers the “isotope effect” in an ECRIS plasmas within
 the model of ion turbulent heating. Получение высоко зарядных ионов очень эффективно в высоко ионизированной нагретой микроволнами плазме в ионном источнике на электронном циклотронном резонансе (ИИЭЦР). Последние экспериментальные результаты показали, что лучшее получение высоко зарядных ионов связано с возникновением слабой ионно-звуковой турбулентности, возникающей благодаря распадной неустойчивости волны накачки в ИИЭЦР. В некоторых теоретических работах были изучены нагрев различных ионов за счет ионно-звуковой турбулентности в ИИЭЦР. При подходящих условиях, благодаря ионно-звуковой неустойчивости в смеси двух различных газов, легкие ионы могут быть нагреты быстрее, чем тяжелые ионы. Удержание ионов лучше при низких ионных температурах, различие в нагреве ионов усиливает потери преимущественно нагретой компоненты легких ионов, уменьшая в то же время потери менее эффективно нагреваемых тяжелых ионов. Появление этого механизма способно объяснить большинство явлений, наблюдающихся в экспериментах с «эффектом газовой смеси». Настоящая статья рассматривает «изотоп-эффект» в плазме ИИЭЦР в модели ионного турбулентного нагрева. Одержання високо зарядних іонів дуже ефективне у високо іонізованій нагрітій мікрохвилями плазмі в
 іонному джерелі на електронному циклотронному резонансі (ІДЕЦР). Останні експериментальні результати
 показали, що краще отримання високо зарядних іонів пов’язане з виникненням слабкої іонно-звукової
 турбулентності, яка виникає завдяки розпадній нестійкості хвилі накачки в ІДЕЦР. В деяких теоретичних
 роботах були вивчені нагрів різних іонів за рахунок іонно-звукової турбулентності в ІДЕЦР. При
 підходящих умовах, завдяки іонно-звуковій нестійкості у суміші двох різних газів, легкі іони можуть бути
 нагріті швидше, ніж важкі іони. Утримання іонів краще при низьких іонних температурах, різниця у нагріві
 іонів підсилює втрати переважно нагрітої компоненти легких іонів, зменшуючи в той же час втрати менш
 ефективно нагріваємих важких іонів. Поява цього механізму здатна пояснити більшість явищ, що
 спостерігаються в експериментах з «ефектом газової суміші». Ця стаття розглядає «ізотоп-ефект» у плазмі ІДЕЦР у моделі іонного турбулентного нагріву. This work was supported by INTAS-01-0373, INTAS
 97.0094, Federal Program “Integration”,
 (№Я0068/2137) and scientific and technical program
 “Education industry” (№ 1535). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Газовый разряд, плазменно-пучковый разряд Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas Слабая ионно-звуковая турбулентность и аномалии изотопов в плазменном ионном источнике на электронном циклотронном резонансе Слабка іонно-звукова турбулентність та аномалії ізотопів у плазмовому іонному джерелі на електронному циклотронному резонансі Article published earlier |
| spellingShingle | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas Ivanov, A.A. Serebrennikov, K.S. Vostrikova, E.A. Wiesemann, K. Газовый разряд, плазменно-пучковый разряд |
| title | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas |
| title_alt | Слабая ионно-звуковая турбулентность и аномалии изотопов в плазменном ионном источнике на электронном циклотронном резонансе Слабка іонно-звукова турбулентність та аномалії ізотопів у плазмовому іонному джерелі на електронному циклотронному резонансі |
| title_full | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas |
| title_fullStr | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas |
| title_full_unstemmed | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas |
| title_short | Weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas |
| title_sort | weak ion sound turbulence and isotope anomaly in electron cyclotron resonance ion source plasmas |
| topic | Газовый разряд, плазменно-пучковый разряд |
| topic_facet | Газовый разряд, плазменно-пучковый разряд |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81159 |
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