Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode
Numeral simulation of an ion bunch (IB) charge influence on a boundary motion of a distributed virtual cathode (VC) has been performed. It has been found that the IB changes the speed of VC boundary movement the more the nearer the IB is to the VC boundary. As a result, the IB can control in certa...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2006 |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode / A.G. Lymar // Вопросы атомной науки и техники. — 2006. — № 2. — С. 82-84. — Бібліогр.: 4 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859621818650853376 |
|---|---|
| author | Lymar, A.G. |
| author_facet | Lymar, A.G. |
| citation_txt | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode / A.G. Lymar // Вопросы атомной науки и техники. — 2006. — № 2. — С. 82-84. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Numeral simulation of an ion bunch (IB) charge influence on a boundary motion of a distributed virtual cathode
(VC) has been performed. It has been found that the IB changes the speed of VC boundary movement the more the
nearer the IB is to the VC boundary. As a result, the IB can control in certain limits the VC border motion.
Проведено численное моделирование влияния заряда ионного сгустка на скорость перемещения границы распределенного виртуального катода. Обнаружено, что заряд ионного сгустка изменяет скорость перемещения границы виртуального катода тем больше, чем ближе ионный сгусток к границе виртуального катода. Этот эффект приводит к тому, что в определенных пределах ионный сгусток может управлять перемещением границы виртуального катода.
Проведено чисельне моделювання впливу заряду іонного згустку на швидкість переміщення межі
розподіленого віртуального катода. Виявлено, що заряд іонного згустку змінює швидкість переміщення
межі віртуального катода тим більше, чим ближче іонний згусток до межі віртуального катода. Цей ефект
призводить до того, що в певних умовах іонний згусток може керувати переміщенням межі віртуального
катода.
|
| first_indexed | 2025-11-29T04:40:11Z |
| format | Article |
| fulltext |
FEATURES OF AN ION BUNCH COLLECTIVE ACCELERATION
BY A BOUNDARY OF A DISTRIBUTED VIRTUAL CATHODE
A.G. Lymar
KIPT, Kharkov, Ukraine
E-mail: lymar@kipt.kharkov.ua
Numeral simulation of an ion bunch (IB) charge influence on a boundary motion of a distributed virtual cathode
(VC) has been performed. It has been found that the IB changes the speed of VC boundary movement the more the
nearer the IB is to the VC boundary. As a result, the IB can control in certain limits the VC border motion.
PACS: 29.17.+w
A method of collective ion acceleration by a poten-
tial overfall, which exists at an interface between two
different states of an electron stream, namely, the state
with and without VC, was presented in [1]. It is shown
experimentally [2] and by means of numeral simulation
[3] that the potential overfall predicted in [1] does exist
and it is possible to speed-up its motion.
The aim of this paper is to study a longitudinal sta-
bility of ions accelerated by a potential overfall and to
estimate an influence of accelerated IB charge on a pro-
cess of acceleration.
An accelerating structure, in which a method of ac-
celeration offered in [1] can be realized, is schematical-
ly presented in Fig.1. It comprises flat parallel elec-
trodes providing a counter propagation of electron
beams (EB). Electrons are accelerated in ‘cathode 1 −
greed 2’ gaps by a potential difference Uk and enter a
drift space between grounded grids.
Fig.1. Scheme of accelerating structure:
1 – cathode; 2 – greed-anode; 3 – counter propagating electron beams
In accordance with [4], the state of stream in space
of drift is determined by the dimensionless value
J=2×Jinj / Jd, where Jinj – is the density of EB injected by
one gap, and Jd is the density of EB, determined by the
3/2 law for the diode in which the applied potential dif-
ference is Uk, and the cathode – anode gap is Y1 – Y0.
As J increases from a zero to J < 4, all the electrons
cross the drift space. At J=4 there is irreversible transi-
tion of stream into the state, when part from the injected
into the drift space electrons comes back to the grids, as if
they were emitted by the cathode located in the drift
space. This EB state one calls the state with VC. After the
origin the state with VC exists at 2.9 <J. At J = 2.9 state
with VC irreversibly passes to the state without VC.
It follows from above said, that there is a hysteresis
of states. For every value of J in the interval of hystere-
sis (2.9<J<4) EB may exist in the VC state or in the
state without VC.
If in the device shown in the Fig.1 J is in the inter-
val of hysteresis, a situation is possible when at x0<x<xb
there is the state without VC, and at xb < x < x1 there is
the state with VC [2, 3]. The coexistence of these states
shows up, generally speaking, in movement the bound-
ary between them. There is only one value of J=3.4,
which the boundary is immobile at. At J >3.4 state with
VC takes in the state without VC, at J <3.4 the state
without VC takes in the state with VC. Speed of the
boundary moving the more, the nearer J to the border of
hysteresis. If J does not depend on x, speed of the
boundary movement is constant, if J = J(x), speed of the
boundary movement also will depend on x.
Since electron charge density in the state without
VC is less than in one with VC, the potential depen-
dence on the x coordinate at the device axes is given by
next shape. Far from a border practically permanent val-
ue of potential, in area of border monotonous transition
is to other more low permanent value. By this overfall
of potential it is possible to accelerate ions. For this pur-
pose it is needed, that the state without VC absorbs the
state with VC with speed increasing along the device. It
can be obtained by the suitable monotonous diminishing
of J in the direction of ions acceleration.
It should be expected that IB charge can influence
on the speed of boundary moving. The numeral simula-
tion of such influencing is conducted by the method of
macroparticles in a cell subject to the condition follow-
ing: the device (fig.1) is unbounded along the z axis, x
component of the electric field at x0 and x1 is equal to
the zero; electrons move only along the axis y; IB is un-
limited along the axis z uniformly charged hard bar with
___________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.82-84.82
the elliptic transversal section. The ratio of longitudinal
axis of ellipse toward transversal one is equal 2, the size
of longitudinal axis is comparable with the size of over-
fall of potential along the axis x. Maximal value of IB
charge density has been chosen from the condition of
possibility of its withholding by the fields of EB and was
-1.7×Q, where Q is the EB charge density at the moment
of injection. The influence of the EB field on IB motion
was not taken into account at the modeling.
Fig.2. Location of overfall of potential vs IB. Near the
curve the charge value in relative units. Position of the
IB center marked by a vertical line
First modeled situation is a mobile overfall and im-
mobile IB for a case, when in the initial moment of time
IB is located in the state without VC. J =3.7, i.e. more
than 3.4, and the state with VC absorbs the state without
VC, the overfall move up to IB. The final states are
shown in Fig.2 for cases, when IB stops motion of the
overfall. It is visible from Fig.2, the more IB charge, the
larger IB distance from the center of the overfall.
Hence, it may conclude, the retarding IB effect on the
overfall is the more the nearer it to the center of the
overfall. The lowest charge value 0.68 is near to the crit-
ical value. At the smaller charge values IB stops to re-
strain the overfall motion. The potential value at the
place of IB location for a curve 0.68 equals to about
1/2Um.
In the next modeled situation J<3.4, the state with-
out VC absorbs the state with VC. IB moves with per-
manent velocity from a region without VC and catches
up the overfall. As calculations show, two variants are
realized: 1) at approaching IB to the overfall the overfall
velocity increased and achieved the IB one. In future
there is their synchronous motion; 2) at the IB velocity
higher than some critical value, IB cross the overfall and
the synchronous motion is not realized.
Fig.3 shows dependences of the overfall velocity
from J at the absence of IB (curve 1) and at the presence
of IB (curve 2). Points of curve 2 a little lower than the
critical IB velocity value. It should be noted that in the
moving system of IB − overfall the loss of control takes
place at the same location IB in relation to the overfall,
as in the case of the immobile system (lower curve in
Fig.2). Thus, stable motion of the system takes place,
when IB located at the x-coordinate, for which the value
of potential is U(x)> 1/2 Um (Fig.2).
Fig.3. Dependence of dimensionless overfall velocity on
the density of EB injection current. 1– overfall without
IB; 2 – is overfall with IB. IB charge = -1.7×Q;
Ve - speed of electrons at injection into the drift space
As seen from Fig.3, IB charge can substantially
change velocity of overfall. If the stable IB acceleration
is possible under these conditions, IB energy at the out-
put may be about four times higher than at IB with a
small charge.
In approaching of small IB charges, the problem of
its longitudinal stability is solved very simply.
Let a charged particle move in the electric field, the
potential of which in the laboratory system of coordi-
nates is described in by the function ( )22atxU − .
Then in the frame of reference, moving with accelera-
tion a in relation to the laboratory system of coordi-
nates, distribution of the potential looks like (see the
Appendix):
( ) ( ) ( ) xaemxUxU ac ⋅+= . (1)
In Fig.4, the dependences built on formula (1) for
the sigmoidal function U(x)=1/(1+ex) at the different
values of coefficient a. are presented.
Fig.4. Potential distribution in the systems of coordi-
nates, which moving with different accelerations a in
relation to the laboratory system of coordinates. For
curve 1 a = 0; the curve number is increased with the
increase in a
As seen from Fig.4, there is an interval of values of
a at which steady acceleration of the charged particle is
possible. It is also evident that in the case of stability
minimum of potential pit and center of IB are located at
the coordinate x, for which ( ) 21<xU .
___________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.82-84.82
As indicated above, the stability of the system over-
fall – IB takes place if 21>U in the IB center location.
Thus, the increase in the IB charge in the accelerating
device with the monotonous diminishing of injected
electrons current density in the direction of IB accelera-
tion is limited by the growth of instability of the system
overfall – IB.
Possibly, this restrictions may be lifted, if to con-
duct acceleration with the by turn changing of foregoing
stabilities, by analogy with the alternating-phase focus-
ing.
APPENDIX
Let a charged particle move in an electric field, po-
tential of which in the laboratory system of coordinates
is described by a function ( ) ( )2, 2atxUtxU −= .
Then the equation of particle motion looks like
( )
x
atxUexm
∂
−∂−= 22
. (A1)
After replacement of variable on a formula
22atx −=ξ Eq. (A1) acquires a kind
( ) ( )
ξ
ξξ
d
dUeam −=+ . (A2)
Multiplying both parts of Eq.(A2) by ξ and integrating,
we will get the expression for the potential in the frame
of reference, moving with acceleration a in relation to
the laboratory system of coordinates
( ) ( )ac
mU U a
a
ξ ξ ξ= + .
REFERENCES
1. A.G. Lymar, V.V. Belikov, A.V. Zvyagintzev, et
al. Method of acceleration of ions // Discovery’s
and Inventions. 1990, №36, p.290 (in Russian).
2. A.G. Lymar, A.V. Zvyagintzev, N.A. Khiznyak.
About a virtual cathode boundary. Preprint KFTI
88-1, 1988 (in Russian).
3. A.G. Lymar. Waves of States in an electron beam
with a distributed virtual cathode // Plasma
Physics. 2003, v.29. №1, p.85 (in Russian).
4. V.R. Bursian, V.I. Pavlov // JRFChS. 1923, v.55,
p.71.
ОСОБЕННОСТИ КОЛЛЕКТИВНОГО УСКОРЕНИЯ
ИОННОГО СГУСТКА ГРАНИЦЕЙ РАСПРЕДЕЛЕННОГО ВИРТУАЛЬНОГО КАТОДА
А.Г. Лымарь
Проведено численное моделирование влияния заряда ионного сгустка на скорость перемещения границы
распределенного виртуального катода. Обнаружено, что заряд ионного сгустка изменяет скорость переме-
щения границы виртуального катода тем больше, чем ближе ионный сгусток к границе виртуального катода.
Этот эффект приводит к тому, что в определенных пределах ионный сгусток может управлять перемещени-
ем границы виртуального катода.
ОСОБЛИВОСТІ КОЛЕКТИВНОГО ПРИСКОРЕННЯ
ІОННОГО ЗГУСТКУ МЕЖЕЮ РОЗПОДІЛЕНОГО ВІРТУАЛЬНОГО КАТОДА
А.Г. Лимар
Проведено чисельне моделювання впливу заряду іонного згустку на швидкість переміщення межі
розподіленого віртуального катода. Виявлено, що заряд іонного згустку змінює швидкість переміщення
межі віртуального катода тим більше, чим ближче іонний згусток до межі віртуального катода. Цей ефект
призводить до того, що в певних умовах іонний згусток може керувати переміщенням межі віртуального
катода.
74
|
| id | nasplib_isofts_kiev_ua-123456789-78773 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-29T04:40:11Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Lymar, A.G. 2015-03-20T20:16:28Z 2015-03-20T20:16:28Z 2006 Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode / A.G. Lymar // Вопросы атомной науки и техники. — 2006. — № 2. — С. 82-84. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 29.17.+w https://nasplib.isofts.kiev.ua/handle/123456789/78773 Numeral simulation of an ion bunch (IB) charge influence on a boundary motion of a distributed virtual cathode (VC) has been performed. It has been found that the IB changes the speed of VC boundary movement the more the nearer the IB is to the VC boundary. As a result, the IB can control in certain limits the VC border motion. Проведено численное моделирование влияния заряда ионного сгустка на скорость перемещения границы распределенного виртуального катода. Обнаружено, что заряд ионного сгустка изменяет скорость перемещения границы виртуального катода тем больше, чем ближе ионный сгусток к границе виртуального катода. Этот эффект приводит к тому, что в определенных пределах ионный сгусток может управлять перемещением границы виртуального катода. Проведено чисельне моделювання впливу заряду іонного згустку на швидкість переміщення межі розподіленого віртуального катода. Виявлено, що заряд іонного згустку змінює швидкість переміщення межі віртуального катода тим більше, чим ближче іонний згусток до межі віртуального катода. Цей ефект призводить до того, що в певних умовах іонний згусток може керувати переміщенням межі віртуального катода. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Линейные ускорители заряженных частиц Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode Особенности коллективного ускорения ионного сгустка границей распределенного виртуального катода Особливості колективного прискорення іонного згустку межею розподіленого віртуального катода Article published earlier |
| spellingShingle | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode Lymar, A.G. Линейные ускорители заряженных частиц |
| title | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode |
| title_alt | Особенности коллективного ускорения ионного сгустка границей распределенного виртуального катода Особливості колективного прискорення іонного згустку межею розподіленого віртуального катода |
| title_full | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode |
| title_fullStr | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode |
| title_full_unstemmed | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode |
| title_short | Features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode |
| title_sort | features of an ion bunch collective acceleration by a boundary of a distributed virtual cathode |
| topic | Линейные ускорители заряженных частиц |
| topic_facet | Линейные ускорители заряженных частиц |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78773 |
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