Enhancement of ion beam charge states by electron vortices in a plasma optical device
We consider the possibility of enhancing the ionization charge states of beam ions by electron vortices excited in cylindrically symmetric plasma optical systems of finite length with crossed radial electric and longitudinal magnetic fields.
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Цитувати: | Enhancement of ion beam charge states by electron vortices in a plasma optical device / A. Goncharov, V. Maslov, I. Brown // Вопросы атомной науки и техники. — 2005. — № 1. — С. 134-136. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-789482015-03-25T03:02:22Z Enhancement of ion beam charge states by electron vortices in a plasma optical device Goncharov, A. Maslov, V. Brown, I. Plasma electronics We consider the possibility of enhancing the ionization charge states of beam ions by electron vortices excited in cylindrically symmetric plasma optical systems of finite length with crossed radial electric and longitudinal magnetic fields. Розглядається можливість доіонизації іонів пучка електронними вихорами, що збуджуються в циліндрично симетричній плазмо-оптичній системі кінцевої довжини зі схрещеною конфігурацією радіального електричного і повздовжнього магнітного полів. Рассматривается возможность доионизации ионов пучка электронными вихрями, возбуждаемыми в цилиндрически симметричной плазмо-оптической системе конечной длины со скрещенной конфигурацией радиального электрического и продольного магнитного полей. 2005 Article Enhancement of ion beam charge states by electron vortices in a plasma optical device / A. Goncharov, V. Maslov, I. Brown // Вопросы атомной науки и техники. — 2005. — № 1. — С. 134-136. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.27.Lw http://dspace.nbuv.gov.ua/handle/123456789/78948 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Plasma electronics Plasma electronics |
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Plasma electronics Plasma electronics Goncharov, A. Maslov, V. Brown, I. Enhancement of ion beam charge states by electron vortices in a plasma optical device Вопросы атомной науки и техники |
| description |
We consider the possibility of enhancing the ionization charge states of beam ions by electron vortices excited in cylindrically symmetric plasma optical systems of finite length with crossed radial electric and longitudinal magnetic fields. |
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Article |
| author |
Goncharov, A. Maslov, V. Brown, I. |
| author_facet |
Goncharov, A. Maslov, V. Brown, I. |
| author_sort |
Goncharov, A. |
| title |
Enhancement of ion beam charge states by electron vortices in a plasma optical device |
| title_short |
Enhancement of ion beam charge states by electron vortices in a plasma optical device |
| title_full |
Enhancement of ion beam charge states by electron vortices in a plasma optical device |
| title_fullStr |
Enhancement of ion beam charge states by electron vortices in a plasma optical device |
| title_full_unstemmed |
Enhancement of ion beam charge states by electron vortices in a plasma optical device |
| title_sort |
enhancement of ion beam charge states by electron vortices in a plasma optical device |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2005 |
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Plasma electronics |
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http://dspace.nbuv.gov.ua/handle/123456789/78948 |
| citation_txt |
Enhancement of ion beam charge states by electron vortices in a plasma optical device / A. Goncharov, V. Maslov, I. Brown // Вопросы атомной науки и техники. — 2005. — № 1. — С. 134-136. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT goncharova enhancementofionbeamchargestatesbyelectronvorticesinaplasmaopticaldevice AT maslovv enhancementofionbeamchargestatesbyelectronvorticesinaplasmaopticaldevice AT browni enhancementofionbeamchargestatesbyelectronvorticesinaplasmaopticaldevice |
| first_indexed |
2025-07-06T03:04:56Z |
| last_indexed |
2025-07-06T03:04:56Z |
| _version_ |
1836865129131540480 |
| fulltext |
ENHANCEMENT OF ION BEAM CHARGE STATES
BY ELECTRON VORTICES IN A PLASMA OPTICAL DEVICE
A. Goncharov1, V. Maslov2 and I. Brown3
1Institute of Physics NASU, Kiev 252650, Ukraine;
2NSC Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine,
E-mail: vmaslov@kipt.kharkov.ua;
3Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
We consider the possibility of enhancing the ionization charge states of beam ions by electron vortices excited in
cylindrically symmetric plasma optical systems of finite length with crossed radial electric and longitudinal magnetic fields.
PACS: 52.27.Lw
INTRODUCTION
Electron vortex structures can be excited in
cylindrically symmetric systems of finite length with
crossed radial electric and longitudinal magnetic fields. In
this paper, we consider the possibility of enhancing the
ionization charge states of beam ions by such electron
vortices. We show that the electron velocity in the vortices
can be sufficiently large to increase the ionization charge
states of beam ions.
The cylindrical configuration that we consider here
makes use of a number of ring electrodes along which an
electric potential is distributed. We show that maximum
ionization is achieved for minimum ion beam velocity
through the vortex region. Though electron-ion collisions
provide ionization, they also result in electron transport, in
turn leading to reduced electron density. Increased
magnetic field results in improved electron confinement.
However, for large magnetic field the electron distribution
is laminar, resulting in reduced ionization. For a given
value of magnetic field, a specific number of discrete
electrodes are required, along which the externally applied
electric potential is distributed, or (alternatively) for a given
number of the electrodes the maximum ionization is
reached at a certain magnetic field.
The experimentally observed dependence of electron
density ne on magnetic field Ho has been analytically
investigated. For Ho less than the optimum magnetic field
Hopt the electron density increases with Ho; for Ho somewhat
greater than Hopt, ne falls with increasing Ho; and for Ho much
greater than Hopt, ne increases with Ho increasing.
We consider the possibility of increasing the
ionization charge states of beam ions by electron vortices
self consistently excited in the plasma-optical system. The
intensity of the excited vortex turbulence is proportional
to magnetic field Ho, and the confinement of electrons is
improved with increased Ho; thus the system calls for
large Ho. It is necessary to use a certain minimum number
of cylindrical electrodes, along which the electric
potential is distributed, so that the radial distribution of
electrons is not layered.
A plasma-optical system for increasing the ionization
state of ions from charge state n up to n+1 by electron
vortices is considered. The system consists of three
cylindrically symmetric segments located axially in the
longitudinal direction (see Fig. 1). The configuration is of
finite length located in the field of a chain of short coils,
the sense of which is such as to create opposing magnetic
fields Ho, and the separate segments trap electrons.
Fig. 1. Schematic of system for increasing ion charge
states
Fig. 2. Longitudinal distribution of electric potential
along each segment
Cylindrical electrodes are also positioned axially, along
which an electric potential Фo is distributed (see Fig. 2).
In each segment the electrons are trapped by Ho and Фo.
The magnetic field structure and the electric potential
distribution due to the ring electrodes along each segment
are shown qualitatively in Fig. 3.
Fig. 3. Magnetic field structure and electric potential
distribution of ring electrodes along one segment of the
system
The system is filled with electrons by secondary
electron emission from ion bombardment of the
cylindrical electrodes by peripheral beam ions. In each
trap volume, crossed electric and magnetic fields are
formed. Such a system is unstable [1-3] and leads to
electron vortex excitation due to the radial gradient of Но.
The interaction of beam ions with vortices can result in
134 Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 134-136
z
ϕ
ϕ
z
r
ϕ
o
ϕ
o
/2ϕ=0
H
o
enhanced ionization of transiting beam ions. In Fig. 4 a
schematic of the concept with vortex electron trajectories
is shown.
Fig. 4. Excitation of electron vortices
Fig. 5. Ionization of beam ions from charge state n
(shown by light circles) up to charge state n+1 (shown by
dark circles) by electron vortices
The electrons can rotate around the axes of the vortices
with significant super-thermal velocities. In Fig. 5 the
ionization of beam ions from charge state n (ions shown
by light circles) up to charge state n+1 (ions shown by
dark circles) by electron vortices is shown schematically.
DEPENDENCE OF RADIAL ELECTRIC
FIELD ON MAGNETIC FIELD
Let us consider the dependence of the radial electric
field that can be supported in the system on Но. We
consider radial collisional electron transport (the
continuous curve in Fig. 6, for Но less than the optimum,
Но<Нopt) and anomalous electron transport (the continuous
curve in Fig. 6 for Но much greater, Но>>Нopt). By Нopt we
mean that derived in [4, 5], for which vortices are not
excited in the system.
We use the fact that the electron density is inversely
proportional to the radial electron velocity ne ~ 1/Vr. In the
collisional case the radial electron velocity is given by Vr
≈ eEorν/meω2
ce, where ν is the electron collision frequency,
Eor is the radial electrical field, and ωce is the electron
cyclotron frequency. From this expression and using that
at Нopt the electron density equals nopt, we find the electron
density for Но<Нopt,
ne = ni/2+[ni
2/4+nopt(nopt–ni)Ho/Hopt]1/2
One can see that ne = nopt at Ho = Hopt, and ne increases with
increasing Ho for Но<Нopt.
Upon excitation of turbulence, the radial electron
transport increases sharply. The saturation amplitude of
the excited vortices is determined by their dissipation rate.
Hence the radial transport velocity Vr is approximately
proportional to the growth rate γ of the instability, i.e. to
the intensity of vortex excitation. For parameters close to
the optimum, slow vortices are excited and γ is
determined by their growth rate γsl . We have
approximately
ne ~ 1/Vr ~ 1/γsl ~ [ℓθ∆n/Ho]-1/3,
ℓθ ~ [(1-η)(∂r(1/ωce)/Voθ]1/2, Voθ ~ ∆n/Ho.
Fig. 6. Dependence of radial electric field on magnetic
field
We derive ne ~ Ho
1/3/[(1-η)ne∆n]1/6. Taking into account
that Η = ηopt(∆n/∆nopt)(Hopt/Ho)2, ηopt = 1. ∆n ≡ noe-noi is the
overcompensation of flow ions by the electrons, we have
ne ~ Ho
1/3/{ne∆n[1-(∆n/∆nopt)(Hopt/Ho)2]}1/6
It can be seen that when Ho exceeds Hopt, ne decreases (the
dash-dot curve in Fig. 6).
For Ho>>Hopt, when the saturation amplitude of the
excited turbulence does not strongly depend on Но, one
can introduce an effective electron collision frequency νef.
Then the velocity of radial motion of the electrons equals
eEorνэфф/meω2
ce . Thus we find that ne-ni ~ Ho.
MAXIMUM ENERGY OF ELECTRON
ROTATION IN A VORTEX
Let us estimate the velocity, δVe, of electron rotation in
a vortex and compare it with the electron drift velocity, Vθ
o = -(e/mωHe)[ez,Ero], in crossed Ero and Ho fields.
One can show [6] that the maximum saturation
amplitude of electric potential in a vortex, φsm, is
φsm ≈ (me/ek2)[ω2
He/2-(∆n/noe)ω2
pe]
where k is the wave vector of the vortex perturbation.
From it an approximate expression follows for the
longitudinal component of rotation of the electron
velocity, which characterizes angular speed Ω ≡ Vθ/r of
their rotation in the vortex field, α≡ezrotV ≈ (ω2
pe/ωHe)δ
ne/neo ≈ ωHe/2. Now taking into account that the vortex
perturbations are unstable and are excited initially with
small azimuth numbers, lθ, the radius of a vortex
approximately equals half the system radius, Rv ≈ R/4. We
find the following approximate expression for δVe
δVe/Vθo ≈ RωHe/4Vθo ≈ (ωHe/ωpe)2(noe/∆n) >> 1.
From the previous ratio we find that the maximum
electron energy due to rotation in the vortex is εe ≈ meR2ω
2
He/32. For experimental parameters such as R = 3.5 cm,
Но = 1000 Oe, one obtains that εe ≈ 62.5 keV. But due to
magnetic field inhomogeneity εe is limited by Фo.
135
H
opt
H
o
E
or
V
V V
V
V V
INCREASING THE ION FLOW RESIDENCE
TIME IN THE SYSTEM
If we use a plateau-type longitudinal distribution of
potential, it is possible to increase considerably the ion
residence time in the system. Then the ion beam velocity
in the system equals Vbi = [(2/mi)(εi-eФo)]1/2 . If the ion
beam energy is only slightly greater than this, εI ≥ eФo ,
then the beam ion transit velocity in the system will be
decreased and the residence time increased.
SYSTEM LENGTH REQUIRED FOR
COMPLETE IONIZATION OF FLOW IONS
TO CHARGE STATE n+1
Let us estimate the minimum length of the system, L ,
for which, during the ion beam propagation with velocity
Vbi through the system, τпр = L/Vbi , there will be complete
ionization of beam ions from charge state n up to charge
state n+1. The time required for additional ionization is
given by τI = 1/niσVe . The ion beam velocity should
exceed Vbi ≥ (2eФo/mi)1/2 for the ion beam propagation
through the system. We choose for the best additional
ionization, Vbi ¿ (2eФo/mi)1/2 . Then the ion residence
time in the system is the longest.
Fig. 7. Dependence of ionization cross section from Ta
2+
to Ta
3+ on electron energy
For complete ionization to charge state n+1 the system
length L should be greater than L ≥ Vbi/Veniσ. Estimations
show that a very long system is necessary for significant
ionization. Therefore we use, instead of an ion beam, a
vacuum-arc plasma flow. In this case there is no necessity
for secondary ion-electron emission, and electrons are
moved with the ion flow. The energy of the streaming ions
is 100 eV. For vortex excitation we use LF wave pumping
of frequency approximately equal to the ion plasma
frequency, similar to HF wave pumping on electron
cyclotron frequency in [7].
To determine L, σ has been calculated (see Fig. 7)
using an expression given in [8]. Using ni = 1012cm-3 and σ
= 0.82 x 10-16cm2 for ionization from Ta
2+ to Ta
3+ we find
that if the amplitude of the vortex electric potential is
limited to Фo, L should be longer than L > 26cm.
CONCLUSION
We have shown that because the magnitude of the
excited vortex perturbation is significantly greater than the
electron cyclotron radius and because the excited fields of
the vortex perturbations are significantly greater than the
radial electrical field of the system, the electron vortex
velocity can considerably exceed the electron drift
velocity in crossed electric and magnetic fields. This
results in the possibility of additional ionization of ions.
These vortices can be enhanced by LF wave pumping at a
frequency approximately equal to the ion plasma
frequency.
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ДОИОНИЗАЦИЯ ИОННОГО ПУЧКА ЭЛЕКТРОННЫМИ ВИХРЯМИ В ПЛАЗМО-ОПТИЧЕСКОЙ
СИСТЕМЕ
А.А. Гончаров, В.И. Маслов, Я. Браун
Рассматривается возможность доионизации ионов пучка электронными вихрями, возбуждаемыми в
цилиндрически симметричной плазмо-оптической системе конечной длины со скрещенной конфигурацией
радиального электрического и продольного магнитного полей.
ДОІОНИЗАЦІЯ ІОННОГО ПУЧКА ЕЛЕКТРОННИМИ ВИХОРАМИ В ПЛАЗМО-ОПТИЧНІЙ
СИСТЕМІ
О.А. Гончаров, В.І. Маслов, Я. Браун
Розглядається можливість доіонизації іонів пучка електронними вихорами, що збуджуються в циліндрично
симетричній плазмо-оптичній системі кінцевої довжини зі схрещеною конфігурацією радіального електричного
і повздовжнього магнітного полів.
136
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