Undulative induction formers of picosecond electron bunches
The basic physical mechanism and the design idea of a new type of Undulative Induction Formers (UNIFs or EH-formers) of especially short intensive electron bunches are proposed and studied. The characteristic feature of the proposed EH-former is the employing of nonstationary crossed linearly polari...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Цитувати: | Undulative induction formers of picosecond electron bunches / V.V. Kulish, I.V. Gubanov, O.A. Orlova // Вопросы атомной науки и техники. — 2001. — № 5. — С. 54-56. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-789812015-03-25T03:02:29Z Undulative induction formers of picosecond electron bunches Kulish, V.V. Gubanov, I.V. Orlova, O.A. The basic physical mechanism and the design idea of a new type of Undulative Induction Formers (UNIFs or EH-formers) of especially short intensive electron bunches are proposed and studied. The characteristic feature of the proposed EH-former is the employing of nonstationary crossed linearly polarized electrical and magnetic undulative fields (EH-fields). Namely, the EH-former turns out to be "opened" for an electron beam only during a very short (picosecond) time interval. A possibility to form rather intensive picosecond electron bunches is shown. Including, the picosecond bunches with a number of electrons in each bunch ~ 10⁸÷10¹⁰. 2001 Article Undulative induction formers of picosecond electron bunches / V.V. Kulish, I.V. Gubanov, O.A. Orlova // Вопросы атомной науки и техники. — 2001. — № 5. — С. 54-56. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS numbers: 29.27.Fh http://dspace.nbuv.gov.ua/handle/123456789/78981 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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The basic physical mechanism and the design idea of a new type of Undulative Induction Formers (UNIFs or EH-formers) of especially short intensive electron bunches are proposed and studied. The characteristic feature of the proposed EH-former is the employing of nonstationary crossed linearly polarized electrical and magnetic undulative fields (EH-fields). Namely, the EH-former turns out to be "opened" for an electron beam only during a very short (picosecond) time interval. A possibility to form rather intensive picosecond electron bunches is shown. Including, the picosecond bunches with a number of electrons in each bunch ~ 10⁸÷10¹⁰. |
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Article |
| author |
Kulish, V.V. Gubanov, I.V. Orlova, O.A. |
| spellingShingle |
Kulish, V.V. Gubanov, I.V. Orlova, O.A. Undulative induction formers of picosecond electron bunches Вопросы атомной науки и техники |
| author_facet |
Kulish, V.V. Gubanov, I.V. Orlova, O.A. |
| author_sort |
Kulish, V.V. |
| title |
Undulative induction formers of picosecond electron bunches |
| title_short |
Undulative induction formers of picosecond electron bunches |
| title_full |
Undulative induction formers of picosecond electron bunches |
| title_fullStr |
Undulative induction formers of picosecond electron bunches |
| title_full_unstemmed |
Undulative induction formers of picosecond electron bunches |
| title_sort |
undulative induction formers of picosecond electron bunches |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2001 |
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http://dspace.nbuv.gov.ua/handle/123456789/78981 |
| citation_txt |
Undulative induction formers of picosecond electron bunches / V.V. Kulish, I.V. Gubanov, O.A. Orlova // Вопросы атомной науки и техники. — 2001. — № 5. — С. 54-56. — Бібліогр.: 6 назв. — англ. |
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Вопросы атомной науки и техники |
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| first_indexed |
2025-07-06T03:06:41Z |
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2025-07-06T03:06:41Z |
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1836865239966023680 |
| fulltext |
UNDULATIVE INDUCTION FORMERS OF PICOSECOND
ELECTRON BUNCHES
V.V. Kulish, I.V. Gubanov1, O.A. Orlova1
Dep. of Physics I, National Aviation University,
1 Komarova Prospect, Kiev, 03058, Ukraine
1 Dep. of Theoretical Physics, Sumy State University,
2 Rymskii-Korsakov St., 44007, Ukraine
The basic physical mechanism and the design idea of a new type of Undulative Induction Formers (UNIFs or
EH-formers) of especially short intensive electron bunches are proposed and studied. The characteristic feature of
the proposed EH-former is the employing of nonstationary crossed linearly polarized electrical and magnetic undu-
lative fields (EH-fields). Namely, the EH-former turns out to be "opened" for an electron beam only during a very
short (picosecond) time interval. A possibility to form rather intensive picosecond electron bunches is shown. In-
cluding, the picosecond bunches with a number of electrons in each bunch ~ 108÷1010.
PACS numbers: 29.27.Fh
1 INTRODUCTION
The problem of forming especially short (including
picosecond) intensive electron bunches with an arbitrary
on-off time ratio is rather argent and topical for the
modern accelerative technology. The manifested interest
is determined by a necessity to observe experimentally a
number of fast processes in various objects of a differ-
ent physical nature [1-5]. Unfortunately, the available
systems of such a type have some important drawbacks,
which limit further extending their application area. Let
us note two of these drawbacks especially. The first is
existing limitations on the bunch density, because of the
influence of the Coulomb electron repulsion mecha-
nism. The second is requirement for the attaining large
magnitudes of the on-off time ratio, including the case
of single electron pulses. This drawback also is connect-
ed with the above-mentioned physical mechanism of
Coulomb electron repulsion.
The new physical and design concepts are proposed
in this paper for overcoming the above-noted difficulties
of traditional systems. The key point of these concepts
is the use of a non-stationary linearly polarized EH-ac-
celerator section [5] as a main basic element of the pi-
cosecond former. We called the proposed system the
EH-formers.
The proposed EH-former has a number of advan-
tages comparing with the known analogous systems [1,
2]. Firstly, it is more compact and characterized by a
simpler design. Secondly, it allows to change smoothly
some key bunch parameters. Including, this gives an op-
portunity to adjust the bunch duration at the output.
And, thirdly, this system can operate with a relatively
large instant bunch current. This, in turn, opens a possi-
bility to form bunches with a large charge density.
Two non-trivial physical mechanisms provide real-
ization of the above-noted EH-former advantages. The
first is the effect of "cutting out" of the picosecond
bunch from a bunch with larger duration. A combina-
tion of two more particular effects put in the basis of the
"cutting out" effect. They are the effect of electron re-
flection in the system input, and the capture effect in the
work bulk of the EH-former [5], respectively. The sec-
ond of the mentioned physical mechanisms is the effect
of dynamic compression. The latter is used for compen-
sation of the Coulomb electron repulsion in the formed
bunch.
2 THE SYSTEM DESCRIPTION
The design block-scheme of the proposed picosec-
ond EH-former is shown in Fig. 1. Here the electron gun
1 forms the nanosecond intensive electron bunches,
which are directed in the input of the section of non-sta-
tionary linearly polarized EH-accelerators 2 [5]. The
forming intensive picosecond punches occurs within
this section. Then, the picosecond bunches enter in the
acceleration section 3. Further compression (due to the
compression effect) and the freezing (owing to increas-
ing electron relativistic mass) take place there. Eventual
acceleration of the formed picosecond bunches (in the
case if it is necessary) is fulfilled within the accelerator
5. It is proposed to construct this accelerator according-
ly with the design scheme of the honeycomb EH-accel-
erators [5].
Fig. 1. Design block-scheme of the picosecond EH-
former. Here: 1 is the electron gun, 2 is the section
of non-stationary linearly-polarized EH-accelera-
tors, 3 is the system for bunch compression and
"freezing", 4 is the output for formed relativistic pi-
cosecond bunches, 5 is the output section of the sta-
tionary honeycomb EH-accelerator.
The design of the section of non-stationary linearly
polarized EH-accelerators 2 (see Fig. 1) is shown in
Fig. 2. Detail description its operation principles is giv-
en in [5]. In what follows, let us analyze the physical
process in this section in more details.
The vector-potential
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
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54
( ) ( ) ( ) ( )∑
=
=
m
j
j
x
jkzjkych
jk
a
tAetzyA
1
sin,,
. (1)
is chosen for description of the forming EH-field [5].
Here k is the wave number, ( ) jatA is the amplitude of
j-th spatial field harmonic, xe is the unite vector along
x-axis, z is the longitudinal coordinate, t is laboratory
time.
Fig. 2. Design of the picosecond electron EH-for-
mer. Here: 1 is the electromagnet poles made of
some ferrite, 2 are gaps between the magnetic poles
1 filled by ceramic inserts, 3 are coils of the electro-
magnets, 4 are the windows in ceramic inserts made
for the electron bunch passing.
Taking into account the well-known relationships
( )ArotB
= , dtAE
∂−= , we can get definitions for the
induction of magnetic field and the intensity of vortex
electrical field, respectively:
{ } ( ) −
⋅= ∑
=
jkzjkychaetAB
m
j
jy sin)(
1
{ } ( )
− ∑
=
jkzjkyshae
m
j
jz cos
1
; (2)
( ) { } ( )jkzjkych
jk
a
tEeE
m
j
j
x sin
1
∑
=
=
. (3)
The generated Coulomb field within the electron
bunch will be calculated using the method of large parti-
cles (the model of particle-particle interactions):
∑∑
==
==
N
j
ij
ij
jN
j
iji r
r
q
EE
1
3
1
, (4)
where ijE
is the intensity of Coulomb electrical field
between some і and j particles, j
q is the j-th charge,
jiij rrr
−= , jir ,
is the coordinates of і-th and j-th parti-
cles, ijij rr
= .
We will use the Hamilton equations for description
of the particle motion in field (1):
tdt
d
∂
∂= HH
;
rdt
d
∂
∂−= HP ;
P
H
∂
∂=
dt
rd
, (5)
here H is the is Hamiltonian, P
is the canonical mo-
mentum.
The Bogolyubov-Zubarev method [6] is used for the
finding asymptotic solution of the problem (5). The so-
lution of equations (3) is looked for in the form
xxx ~+= , where x is averaged value, and x~ is oscilla-
tive parts of the calculated values [6]. Calculations are
done in the first approximation of the method, confining
by the terms no higher the cubic (with respect to the am-
plitude of EH-field (1)) order.
3 ANALYTICAL ANALYSIS
Let us analyze shortly the physics of the system un-
der consideration. The relevant calculation allows to
clear up the detail scenario of the above-discussed effect
of "cutting out" of the picosecond bunch from a bunch
with larger duration. It is found that only those particles
form the picosecond bunch, which enter in the system
input at the time moment, when the magnetic field in-
duction is approximately equal to zero. The rest of parti-
cles are reflected from the system input. Therein, part of
the passed particles are further “captured” in the accel-
eration channel because the increasing of the magnetic
field on time. As a result, the picosecond bunch is
formed within the accelerative channel.
Inasmuch as the magnetic field changes during the
bunch forming process the velocities of the "last" parti-
cles in the bunch are found to be somewhat higher than
the particle velocities of the front part of the bunch. This
phenomenon we called as the effect of inverse bunch
modulation. As a result the particles of the back part of
the bunch have trend to catch up the front bunch parti-
cles. As a sequence, the effect of dynamic bunch com-
pression realizes in the system.
Let us introduce the "closing time" 01τ and the
"opening time 02τ of the system input. After required
calculation we obtain:
{ } { }
β
±−=τ 3
030
0
02,01
111
2
Ksh
KcheE
p
, (6)
where cv00 =β , 0v is the electron velocity in the
system input, . 003 2cpLeEK = , L is the system
length, 0p is the electron mechanical momentum in the
input. The relationship (6) allows to calculate the dura-
tion of the “cut out” bunch
{ }
{ }3
3
3 Kch
Ksh
K
tr
input
τ
=τ∆ , (7)
where 0vLtr =τ . It is readily seen that the vortex
electric field plays an important role in the cutting out
process. Let us analyze relationship (7) in the following
two limited case. The first is the case 13 > >K (case of
strong electric field). After simple calculation it is easily
to obtain (non-relativistic case 10 < <β ):
03 2 eEmcKtrinput ≅τ≅τ∆ , (8)
i.e., the stronger is electric field the less is duration of
the “cut out” bunch in the input. The second is the case
of weak electric field 13 < <K :
trinput τ≅τ∆ , (9)
in the case only if cuptr τ≤τ , where cupτ is the capture
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 55-56.
55
time [5].
The compression effect could be illustrated by the
dependency of the non-dimension output electron veloc-
ity outβ on its fly-in time in the system input τ (the
Coulomb electron interactions is neglected):
( )
{ } { }
2
3
2
043
2
0
1
1
1
⋅τ⋅β−+
β−
−=τβ
KshKKch
out (10)
where 2
04 2mceEK = . It is readily seen that in-
deed, the less is the fly-in time τ the higher is the out-
put electron velocity outcβ .
4 NUMERICAL ANALYSIS
In what follows, let us discuss the forming process
in the dense picosecond bunches. The Coulomb interac-
tions play important role in this case. We take they into
account further. Let us use the numerical modeling of
the process considered in combination with the method
of large particles. Calculation of the Coulomb electric
field is accomplished in accordance with the above-de-
scribed scheme (see definition (4) and corresponding
commentaries). The results of numerical modeling are
shown in Fig. 3 and in Tab. 1.
Table 1. Results of project analysis of the EH-former
Parameters Values
Induction of the magnetic field, kGs 2.65
Intensity of the vortex electrical
field, MV/m
1.7
Period of undulation, cm 11
Length of the system, m 65
Bunch energy in the output, keV 240
A number of electrons in the bunch ~109
The spatial distribution of the formed bunch is il-
lustrated in Fig. 3. As it is easily seen, the proposed
forming system allows to form quasi-stable bunches
with a peak density ~ 2.3·10-8 mm-3. The latter corre-
sponds to number of electrons in the bunch ~109.
It should be mentioned that the result obtained is
the best from the analogous ones, which can provide tra-
ditional picosecond formers with a large on-off time ra-
tio. Let us illustrate this affirmation by the following
example. The Department of Energy of the United
States has announced at beginning of 2000 the competi-
tion (Program Solicitations, DOE/SC-0008, Section 36
"Advanced Concepts and Technology for High Energy
Physics Accelerators") on developing a "relatively inex-
pensive" (no more expensive than $1million) system for
forming picosecond bunches with a high density of
charge. The required parameters of the announced sys-
tem are close to the above obtained. So, the proposed
EH-former could be used for successful solving the an-
nounced problem.
Fig. 3. Spatial distribution of the formed high-densi-
ty electron bunch. Here: induction of the magnetic
field is 2.65 kGs, intensity of the vortex electrical
field is 1750 kV/m, period of undulation is 11 cm,
length of the system is 65 cm, beam energy in the in-
put is 100 keV, current strength of the input beam is
50 A, a number of electrons in the output bunch
is ~109.
6 CONCLUSION
Thus, a new concept for construction of the system
for forming intensive picosecond bunches with a large
on-off time ratio (EH-former) is proposed and substanti-
ated. The accomplished analysis showed that the combi-
nation of the two specific physical mechanisms forms
the basis of the proposed formers. The first is the effect
of "cutting out" the picosecond bunch from a bunch
with larger duration. The second is the effect of dynam-
ic compression of the formed electron bunch. The
physics of both these effects is studied in this paper.
REFERENCES
1. Ya.S.Umansky. Radiography of metals and semi-
conductors. Moscow: Nauka, 1969 (in Russian).
2. V.V.Nemoshkalenko. X-ray emission spectroscopy
of metals and alloys. Kyiv: Naukova Dumka, 1972
(in Ukrainian).
3. I.G.Artuh, G.N.Kamaldinova. Free electron laser.
Parts I, II. Moscow: CSRI “Electronika”, 1988.
4. A.K.Krasnih, I.V.Kuznetsov, E.A.Perelshtein.
Method of forming high-current ultra-relativistic
electron bunches of sub-nanosecond range and the
device for its realization. Patent №3819456/24-21
SU, 5 H 05 H 5/ 00. Priority 30. 11.84, № 1266452
A1, public. 30.09.90 bull. №36.
5. V.V.Kulish, P.B.Kosel, A.G.Kailyuk, I.V.Gubanov.
New acceleration principle of charged particles for
electronic applications. Examples // The Interna-
tional Journal of Infrared and Millimeter Waves.
1998, v. 19, № 2, p. 251-328.
6. V.V.Kulish. Methods of averaging in nonlinear
problem of relativistic electrodynamics. Tampa, At-
lanta: World Federation Published Company, Inc.
1996.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5
Серия: Ядерно-физические исследования (39), с. 56-56.
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