Hysteresis effects in electron guns
Computer simulations of beam formation in an electron gun with large compression of a thin annular beam show some hysteresis effects: a beam with different currents can exist in the same external conditions. The results of computer simulation are presented for several simple drift and diode geomet...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2004 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2004
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/79327 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Hysteresis effects in electron guns / A.V. Agafonov, A.N. Lebedev // Вопросы атомной науки и техники. — 2004. — № 2. — С. 50-52. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859631960302813184 |
|---|---|
| author | Agafonov, A.V. Lebedev, A.N. |
| author_facet | Agafonov, A.V. Lebedev, A.N. |
| citation_txt | Hysteresis effects in electron guns / A.V. Agafonov, A.N. Lebedev // Вопросы атомной науки и техники. — 2004. — № 2. — С. 50-52. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Computer simulations of beam formation in an electron gun with large compression of a thin annular beam show
some hysteresis effects: a beam with different currents can exist in the same external conditions. The results of
computer simulation are presented for several simple drift and diode geometry and for the gun with large
compression of an annular beam. Physics reasons of such behaviour are discussed.
При дослідженні нестаціонарного режиму формування тонкостінного електронного пучка з великою
компресією по радіусі виявлені гістерезисні ефекти: при тих самих зовнішніх умовах струм пучка може
приймати різні значення. Приведено результати чисельного моделювання формування пучків для декількох
простих дрейфових і діод них геометрій, і для гармати з великою компресією пучка. Обговорюються фізичні
причини гістерезисних ефектів. Робота виконана за підтримкою РФФД по гранту 03-02-17301.
При исследовании нестационарного режима формирования тонкостенного электронного пучка с
большой компрессией по радиусу обнаружены гистерезисные эффекты: при одних и тех же внешних условиях ток пучка мог принимать разные значения. Приведены результаты численного моделирования формирования пучков для нескольких простых дрейфовых и диодных геометрий, и для пушки с большой компрессией пучка. Обсуждаются физические причины гистерезисных эффектов. Работа выполнена при поддержке РФФИ по гранту 03-02-17301.
|
| first_indexed | 2025-12-07T13:11:48Z |
| format | Article |
| fulltext |
HYSTERESIS EFFECTS IN ELECTRON GUNS
A.V.Agafonov and A.N.Lebedev
Lebedev Physical Institute, Leninsky pr. 53, Moscow, V-333, GSP-1, 119991, Russia
E-mail: agafonov@sci.lebedev.ru, lebedev@sci.lebedev.ru
Computer simulations of beam formation in an electron gun with large compression of a thin annular beam show
some hysteresis effects: a beam with different currents can exist in the same external conditions. The results of
computer simulation are presented for several simple drift and diode geometry and for the gun with large
compression of an annular beam. Physics reasons of such behaviour are discussed.
Work supported by RFBR under grant 03-02-17301.
PACS: 29.25.Bx
1. INTRODUCTION
Recently one begun to use photocathodes that permit
forming "cold" beams in sources of electron beams of
high brightness developed and applied for FELs and lin-
ear colliders. One of the important problems in these in-
vestigations concerns the value of the current taken
from the photocathode. In a number of works − theoret-
ical as well as experimental − there is discussed the pos-
sibility of obtaining currents exceeding the Child-Lang-
muir limit and is indicated that such an increase is pos-
sible only for the generation of short bunches the length
of which is less or of the order of the gap length.
Naturally, the classical CL-law is applicable only for
a stationary regime with the current limited by the space
charge for the following conditions: 1) voltage constant,
2) transverse dimensions of the emitting surface signi-
ficantly exceeding (geometry close to unidimensional)
the characteristic longitudinal dimensions of the acceler-
ating region and 3) emissive power of the cathode un-
limited.
Let us consider two first of the limitations. The first
corresponds to the current constancy and implicitly im-
plies that the variable quantity can be only the voltage,
while the current value determined by this voltage. It
should be noted that with the appearance of efficient
photoemitters and lasers, it became possible to vary in-
dependently the emission current, in addition to the pos-
sibility of varying the voltage. The possibility of con-
trolling the beam current in photoemission sources at a
fixed voltage leads to a qualitatively different situation.
To a certain extent it is suggestive of the process of
beam injection (although at a very low initial energy) in
an accelerating region rather than drawing the beam
from an emitting surface.
The second limitation reduced the problem to unidi-
mensional and, evidently, is violated under real condi-
tions. Although the influence of the end effects is recog-
nised, its contribution is considered to be small. At the
same time, in a plane diode, when the transverse dimen-
sions of the emitter are approximately equal to the
length of the gap, the influence of fringe effects be-
comes determining. They are no longer simply fringe
effects, they are main effects.
In view of the non-stationary nature and multidimen-
sionality of the problem, the results given below were
obtained by computer simulation with electromagnetic
code KARAT [1].
2. FRINGE EFFECTS IN SIMPLE DRIFT
AND ACCELERATING REGIONS
For a purely stationary flow that is one-dimensional
and unlimited in the transverse direction, the depend-
ence of the passing current Iout on injection current Iinj is
represented by the so-called "lambda-curve" (Fig. 1) [2].
Fig.1. λ-curve
Three solutions are possible for the region from Icr1
to Icr2 in such a flow. One of these is with a virtual cath-
ode and partial passage of the beam (lower part of solid
curve) and the other two (merging into one) are without
a virtual cathode and with complete passage of the
beam. It is considered that the last two states are un-
stable and when Icr1 is exceeded the beam always goes
to the lower part of the curve with formation of a virtual
cathode. For unlimited increase of injected current the
virtual cathode asymptotically approaches the plane of
injection and through the region there passes only cur-
rent equivalent to the CL-current for a plane diode of
the same dimensions, with voltage corresponding to the
energy of injected electrons. For non-relativistic energy
of particles, Icr1 = 4 ICL, Icr2 = 2 Icr1.
In [3], it was analytically shown that when the flow
completely fills the chamber cross-section (the case of a
semi-infinite plane slit with end plane was considered),
the current passed can increase without limit Iout ∝
(Iinj)1/2 due to "exudation" of particles close to the
chamber wall in a thin layer. The thickness of this layer
decreases inversely proportionally to (Iinj}1/2. Close to
the end plane, the central part of the beam is blocked by
the space-charge field and the virtual cathode acquires
the form of such a coaxial slit with rounded edges.
Let us consider the case when two-dimensional ef-
fects appear most effective. The drift region is chosen in
the form of a cylindrical resonator having the diameter
(D=5 cm) much larger than the longitudinal dimension
(d=1 cm), the diameter of injected beam (2re=1 cm)
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.50-52. 50
equals to the length of the resonator. We present the res-
ults for a beam having non-relativistic energy
W=20 keV. In Fig.1, the value of current is presented in
units corresponding to CL-current (ICL = π re
2 jCL, jCLd2 =
6.6 A for 20 kV on the diode). The solid line show the
analytical dependence for one-dimensional stationary
flow and the dotted lines the calculated dependence for
established regime when injecting beams of various cur-
rents with a 4-ns linear front. The established beam con-
figuration for 200-A injected current is shown in Fig.2
and is very similar to that considered in [3].
Fig.2. Beam with "whiskers"
The difference is that the beam passes far from the side
walls and the passed current does not increase with the
injected, but remains approximately at one level. It
should be noted that the main part of the current is con-
centrated in "whiskers", the thickness of which de-
creases with increasing injected current.
The time dependence of the current passing through
the resonator is shown in Fig.3. The interruption of current
is due to the formation of a virtual cathode arising near the
center of the resonator and is rapidly displaced toward the
injection plane when reflected electrons appear.
With increasing transverse dimensions the influence
of "whiskers" on the inner part of the beam is weakened
due to preventing of field by electrodes and electrons
with density of current close to the Child-Langmuir be-
gin take "emitted" from the virtual-cathode region.
Since the total CL-current will increase proportionally
to r2 and the current in the "whiskers" not more than r,
the contribution of the "whiskers" becomes small relat-
ive to current from a larger area, but lower current dens-
ity. This corresponds to one-dimensional flow unlimited
in the transverse direction.
Fig.3. Transient regime in the drift region
The detailed exposition of the effects occurring in a
drift region had to show, as its main purpose, that qualit-
ative concepts about the formation of beam structure in
the drift region can be transferred to the accelerating re-
gion. In any case, this is so when it is possible to rapidly
control emission current, i.e., for the case of photocath-
odes.
Fig.4. Transient regime in the plane diode
The formation of "whiskers" in a drift region occurs
particularly effectively when near the cathode boundary
there is a conducting wall and particles simply drift
along it with the energy close to the energy of injection.
In the case of an accelerating region, the energy of emit-
ted electrons is low and the formation of fringe
"whiskers" becomes difficult because of the low energy
of "injection" and strong influence of the proper field.
The proximity of the electrode, at the cathode potential,
directly to the boundary of the emitting surface leads to
screening of the proper as well as extracting field. Thus,
it is necessary that the distance of side walls from emit-
ter edges be such as to allow, on the one hand, consider-
able screening the influence of own space charge and,
on the other, penetration of a sufficiently large external
field.
As an example that supports such an approach, we
present in Fig.4,5 time dependencies of the beam cur-
rent in a plane diode and in a diode with emitting sur-
face in a recess. The voltage on the diode is constant
and equal to 20 kV, emitter diameter is 1 cm, emission
current increases linearly to 8 A in 4 ns and is then held
constant. In the first case, the hysteresis is practically
imperceptible, but in the second case it is quite pro-
nounced.
Fig.5. Transient regime in the conical diode
3. HYSTERESIS EFFECTS IN THE HIGH-
VOLTAGE ELECTRON GUN
Spatial-temporal hysteresis effects to a significant
extent appeared in the process of developing an electron
gun with large compression of a tubular beam (Fig.6)
intended for generation of powerful microwave and IR
radiation [4].
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.50-52.51
Fig.6. Schematic diagram of the gun
An electron gun has been designed to produce a
beam for generation of high-power microwaves and IR-
radiation. It has the following design parameters: energy
of electrons 350...450 keV, beam current >100 A, lon-
gitudinal momentum spread <1%, pulse duration 10 µs,
repetition rate up to 10 Hz.
A plane, ring-shaped, cathode, having a 28-mm av-
erage radius and a 6...8 mm width, is used to produce an
annular beam. The cathode surface is screened by two
focusing electrodes to operate in a space-charge limited
regime. The focusing system must form a laminar beam
inside the accelerating gap at rather low magnetic field
and transport the beam to an experimental region of
about 50-cm length. Within this region, the beam radius
is 2.5 mm and annular thickness is less than 1 mm due
to a large magnetic field of 15 kGs.
The code KARAT was used to calculate the beam
dynamics and the results were tested by means of the
stationary code SAM [5]. Simulation of emission of
particles in the KARAT code could be realised by two
methods: giving constant (or variable) emission current
exceeding the space-charge limited current and increas-
ing the voltage on the gun to a certain given value (ther-
mionic cathode); giving constant voltage on the gun and
increasing emission current from the cathode in time in
accordance with a desired law (photocathode).
Fig.7 shows the averaged (high-frequency compon-
ents filtered off) behaviour of beam current at the gun
output for various modelling conditions. Dependencies
1-3 correspond to conditions of photocathode operation
and dependence 4 to conditions of thermionic cathode
operation. Dependencies 1-3 were obtained for the con-
stant rate of emission current increase (about 28 A/ns)
on the linear front, the duration of which was 7 ns
(195 A), 7.5 ns (210 A) and 11 ns (310 A) for depend-
encies 1-3, respectively, and the constant current for
greater time. Current discrimination is clearly seen at
195 A, with subsequent drop to values that approxim-
ately correspond to the beam current value in the sta-
tionary state obtained with stationary code SAM. The
fourth dependence is plotted for the case when the emis-
sion current is held constant at 400 A while the voltage
on the diode increases from 160 kV to 400 kV in 8 ns.
Fig.7. Hysteresis effects in the high-voltage gun
It should be noted that a little screening of the cath-
ode (for example, placing it in a 5-mm deep circular
slot), leading of course to a decrease in diode perveance,
is accompanied by a sharper change in the ratio of peak
to stationary value of current.
4. CONCLUSIONS
Computer simulations of beam formation in the gun
show some hysteresis effects: a beam with a different
current can exist in the same external conditions. At the
upper (metastable) part of a hysteresis curve the beam
current exceeds the Child-Langmuir current. Experi-
mental observation of these metastable states is possible
if one has the possibility for fast control of emitted cur-
rent, which is the case for photoemission cathode.
REFERENCES
1. P.V.Kotetashwily, P.V.Rybak, V.P.Tarakanov. In-
stitute of General Physic: Preprint No.44, Moscow,
Russia. 1991.
2. H.V.Ivey // Adv. Electronic and Electron Physics.
1954, v.6, p.137.
3. V.S.Voronin, A.N.Lebedev, Yu.T.Zozula Sov. //
JTP, 1972, v.42, p.546.
4. A.V.Agafonov, E.G.Krastelev, A.N.Lebedev et al.
// Proceedings of the 10th Intern. Conference on
High Power Particle Beams, San Diego, USA.
1994, v.2, p.522.
5. M.A.Tiunov, B.M.Fomel, V.P.Yakovlev. Institute
of Nuclear Physics: Preprint No.87-35, Novos-
ibirsk, Russia, 1987.
ГИСТЕРЕЗИСНЫЕ ЯВЛЕНИЯ В ЭЛЕКТРОННЫХ ПУШКАХ
А.В. Агафонов, А.Н. Лебедев
При исследовании нестационарного режима формирования тонкостенного электронного пучка с
большой компрессией по радиусу обнаружены гистерезисные эффекты: при одних и тех же внешних усло-
виях ток пучка мог принимать разные значения. Приведены результаты численного моделирования фор-
мирования пучков для нескольких простых дрейфовых и диодных геометрий, и для пушки с большой ком-
прессией пучка. Обсуждаются физические причины гистерезисных эффектов. Работа выполнена при под-
держке РФФИ по гранту 03-02-17301.
ГІСТЕРЕЗИСНІ ЯВИЩА В ЕЛЕКТРОННИХ ПУШКАХ
А.В. Агафонов, А.М. Лебедєв
При дослідженні нестаціонарного режиму формування тонкостінного електронного пучка з великою
компресією по радіусі виявлені гістерезисні ефекти: при тих самих зовнішніх умовах струм пучка може
приймати різні значення. Приведено результати чисельного моделювання формування пучків для декількох
простих дрейфових і діод них геометрій, і для гармати з великою компресією пучка. Обговорюються фізичні
причини гістерезисних ефектів. Робота виконана за підтримкою РФФД по гранту 03-02-17301.
52
|
| id | nasplib_isofts_kiev_ua-123456789-79327 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:11:48Z |
| publishDate | 2004 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Agafonov, A.V. Lebedev, A.N. 2015-03-31T09:12:55Z 2015-03-31T09:12:55Z 2004 Hysteresis effects in electron guns / A.V. Agafonov, A.N. Lebedev // Вопросы атомной науки и техники. — 2004. — № 2. — С. 50-52. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 29.25.Bx https://nasplib.isofts.kiev.ua/handle/123456789/79327 Computer simulations of beam formation in an electron gun with large compression of a thin annular beam show some hysteresis effects: a beam with different currents can exist in the same external conditions. The results of computer simulation are presented for several simple drift and diode geometry and for the gun with large compression of an annular beam. Physics reasons of such behaviour are discussed. При дослідженні нестаціонарного режиму формування тонкостінного електронного пучка з великою компресією по радіусі виявлені гістерезисні ефекти: при тих самих зовнішніх умовах струм пучка може приймати різні значення. Приведено результати чисельного моделювання формування пучків для декількох простих дрейфових і діод них геометрій, і для гармати з великою компресією пучка. Обговорюються фізичні причини гістерезисних ефектів. Робота виконана за підтримкою РФФД по гранту 03-02-17301. При исследовании нестационарного режима формирования тонкостенного электронного пучка с большой компрессией по радиусу обнаружены гистерезисные эффекты: при одних и тех же внешних условиях ток пучка мог принимать разные значения. Приведены результаты численного моделирования формирования пучков для нескольких простых дрейфовых и диодных геометрий, и для пушки с большой компрессией пучка. Обсуждаются физические причины гистерезисных эффектов. Работа выполнена при поддержке РФФИ по гранту 03-02-17301. Work supported by RFBR under grant 03-02-17301. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Элементы ускорителей Hysteresis effects in electron guns Гістерезисні явища в електронних пушках Гистерезисные явления в электронных пушках Article published earlier |
| spellingShingle | Hysteresis effects in electron guns Agafonov, A.V. Lebedev, A.N. Элементы ускорителей |
| title | Hysteresis effects in electron guns |
| title_alt | Гістерезисні явища в електронних пушках Гистерезисные явления в электронных пушках |
| title_full | Hysteresis effects in electron guns |
| title_fullStr | Hysteresis effects in electron guns |
| title_full_unstemmed | Hysteresis effects in electron guns |
| title_short | Hysteresis effects in electron guns |
| title_sort | hysteresis effects in electron guns |
| topic | Элементы ускорителей |
| topic_facet | Элементы ускорителей |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79327 |
| work_keys_str_mv | AT agafonovav hysteresiseffectsinelectronguns AT lebedevan hysteresiseffectsinelectronguns AT agafonovav gísterezisníâviŝavelektronnihpuškah AT lebedevan gísterezisníâviŝavelektronnihpuškah AT agafonovav gisterezisnyeâvleniâvélektronnyhpuškah AT lebedevan gisterezisnyeâvleniâvélektronnyhpuškah |