Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production
Experiment performed on plasma synchrotron Gyrac-X operating on synchrotron gyromagnetic autoresonance (SGA) is described. Gyrac-X is a compact plasma x-ray source in which kinetic energy of relativistic electrons obtained under SGA converts into x-ray by falling e-bunches on to a heavy metal target...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Цитувати: | Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production / V.V. Andreev, A.M. Umnov // Вопросы атомной науки и техники. — 2000. — № 1. — С. 3-7. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-815402015-05-31T19:49:33Z Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production Andreev, V.V. Umnov, A.M. Релятивистская плазменная элeкtрoника Experiment performed on plasma synchrotron Gyrac-X operating on synchrotron gyromagnetic autoresonance (SGA) is described. Gyrac-X is a compact plasma x-ray source in which kinetic energy of relativistic electrons obtained under SGA converts into x-ray by falling e-bunches on to a heavy metal target. The plasma synchrotron acts in a regime of a magnetic field pulse packet under constant level of microwave power. Experiments and numerical modeling of the process showed that such a regime allowed obtaining dense short lived relativistic electron bunches with average electron energy of 500 keV – 4.5 MeV. Parameters of the relativistic electron bunch (energy, density and volume) and dynamics of the electron bunches can be controlled by varying the parameters of the SGA process. Possibilities of x-ray intensity increase are also discussed. 2000 Article Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production / V.V. Andreev, A.M. Umnov // Вопросы атомной науки и техники. — 2000. — № 1. — С. 3-7. — Бібліогр.: 7 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/81540 533.9 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Релятивистская плазменная элeкtрoника Релятивистская плазменная элeкtрoника |
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Релятивистская плазменная элeкtрoника Релятивистская плазменная элeкtрoника Andreev, V.V. Umnov, A.M. Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production Вопросы атомной науки и техники |
| description |
Experiment performed on plasma synchrotron Gyrac-X operating on synchrotron gyromagnetic autoresonance (SGA) is described. Gyrac-X is a compact plasma x-ray source in which kinetic energy of relativistic electrons obtained under SGA converts into x-ray by falling e-bunches on to a heavy metal target. The plasma synchrotron acts in a regime of a magnetic field pulse packet under constant level of microwave power. Experiments and numerical modeling of the process showed that such a regime allowed obtaining dense short lived relativistic electron bunches with average electron energy of 500 keV – 4.5 MeV. Parameters of the relativistic electron bunch (energy, density and volume) and dynamics of the electron bunches can be controlled by varying the parameters of the SGA process. Possibilities of x-ray intensity increase are also discussed. |
| format |
Article |
| author |
Andreev, V.V. Umnov, A.M. |
| author_facet |
Andreev, V.V. Umnov, A.M. |
| author_sort |
Andreev, V.V. |
| title |
Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production |
| title_short |
Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production |
| title_full |
Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production |
| title_fullStr |
Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production |
| title_full_unstemmed |
Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production |
| title_sort |
generation of relativistic electron bunches in plasma synchrotron gyrac-x for hard x-ray production |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2000 |
| topic_facet |
Релятивистская плазменная элeкtрoника |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/81540 |
| citation_txt |
Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production / V.V. Andreev, A.M. Umnov // Вопросы атомной науки и техники. — 2000. — № 1. — С. 3-7. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT andreevvv generationofrelativisticelectronbunchesinplasmasynchrotrongyracxforhardxrayproduction AT umnovam generationofrelativisticelectronbunchesinplasmasynchrotrongyracxforhardxrayproduction |
| first_indexed |
2025-07-06T06:34:13Z |
| last_indexed |
2025-07-06T06:34:13Z |
| _version_ |
1836878301318086656 |
| fulltext |
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000. №1.
Серия: Плазменная электроника и новые методы ускорения (2), с. 3-7.
3
UDK 533.9
GENERATION OF RELATIVISTIC ELECTRON BUNCHES IN PLASMA
SYNCHROTRON GYRAC-X
FOR HARD X-RAY PRODUCTION
V.V.Andreev, A.M. Umnov
Plasma Physics Laboratory, Peoples’ Friendship University of Russia, Moscow, Russia,
e-mail: aumnov@sci.pfu.edu.ru
– Experiment performed on plasma synchrotron Gyrac-X operating on synchrotron gyromagnetic
autoresonance (SGA) is described. Gyrac-X is a compact plasma x-ray source in which kinetic energy of
relativistic electrons obtained under SGA converts into x-ray by falling e-bunches on to a heavy metal
target. The plasma synchrotron acts in a regime of a magnetic field pulse packet under constant level of
microwave power. Experiments and numerical modeling of the process showed that such a regime allowed
obtaining dense short lived relativistic electron bunches with average electron energy of 500 keV – 4.5
MeV. Parameters of the relativistic electron bunch (energy, density and volume) and dynamics of the
electron bunches can be controlled by varying the parameters of the SGA process. Possibilities of x-ray
intensity increase are also discussed.
1. Introduction
Synchrotron gyromagnetic autoresonance (SGA) is
electron cyclotron resonance (ECR) in plasma confined
in a simple mirror trap in a magnetic field smoothly
growing in time. Unlike ECR in case of SGA the
relativistic change of the electron mass is compensated
with the change of the magnetic field in time
B(t)=B0[1+b(t)] (B0=m0cω/e, m0 and e are the rest mass
and the charge of the electron, ω - angular frequency of
HF field, b(t) - monotonically growing function of time.
As a consequence the resonant condition ceωω ≅ (ωce
= eB(t)/m0γc, γ = (1 − v2/c2)-1/2, v – velocity of the
electron) is maintained automatically. Under SGA the
electron phase ϕ (phase is the angle between the vector
of electric field strength E and the vector of the impulse
of the electron p) is being trapped into such an interval
that average time energy of the electron grows in
accordance with the law of the magnetic field growth:
)()( tbtW ≅ , where 1−=γW – kinetic energy of the
electron in 2
0cm units. The maximum value of energy
of electrons gained during SGA is limited only by
radiation loss. The average electron energy is
determined by the value of the magnetic field and
doesn't depend on the microwave field strength:
[ ]1/)(511)(~
0 −⋅≅ BtBkeVW .
The possibility of such a process was shown
theoretically [1] and experimentally [2, 3, 7].
Experiments performed on plasma synchrotrons Gyrac-
0, Gyrac-D and Gyrac-X as well as simulation of SGA
show that variation of SGA parameters (initial plasma
density and its dimension, electric field strength,
velocity of magnetic field growth) gives a possibility of
obtaining of different plasma objects. In case of
comparatively small initial radial plasma size and
plasma density one can obtain an accelerated bunch of
electrons. In cases of greater plasma dimension and
density relativistic plasma formation is generated. The
work is aimed to experimental and numerical study of
relativistic electron bunches generation and their
transportation to a heavy metal target for x-ray
production.
2. Experimental device
Gyrac-X is a plasma x-ray source in which
kinetic energy of relativistic electrons obtained
under SGA converts into x-ray by falling of electron
bunches on to a heavy metal target.
Fig. 1. Sketch of the Gyrac-X plasma
synchrotron
A sketch of Gyrac-X is represented in Fig. 1.
The TE111 cavity is exited by microwave at the
frequency 2.4 GHz, 350 W. The static magnetic
mirror field produced by coils (L=15 cm, 05.1≅R )
satisfies the ECR condition in the midplane of the
cavity. Pulse coils produce the pulse magnetic field:
μs)500100( tincr −≅ , G B 500max ≅ . The stainless
wall of the cavity allows penetration of pulse
magnetic field with a small decrease of its strength.
Electromagnets used in Gyrac-X experiments
give it possible to form static magnetic field profiles
for different experimental scenarios: 1) increasing
pulse magnetic field [2, 3], 2) reverse pulse
magnetic field [6]. The obtained experimental data
showed that in the first case SGA-trapping is greater
by factor of 2 in comparison with the case of reverse
magnetic field. The installation allows running the
heating process in the regime of a pack of SGA-
4
pulses [6] but under constant level of microwave
power.
Diagnostic of the relativistic plasma produced
were performed by undertaking analysis of the
bremsstrahlung radiation from gas as well as from a
W-target (1.5x1.5mm2) placed into relativistic
plasma area. X-ray measurement were made by a
NAI(Tl) scintillator spectrometer (crystal 25x25
mm2, the detection efficiency of photons with
energy 100-300 KeV is no less than 50%) in the
regimes of amplitude analysis and registration of x-
ray total photon flux intensity. The x-ray detector
system was calibrated against a primary standard -
γ-source Cs137, Na22 of known intensities. The
collimated x-ray telescope collects photons from a
volume of hot-electron location. The electron bunch
radial dimension was defined by bremsstrahlung
photon flux from the target moving along the radius.
Diagnostics of produced relativistic plasma were
performed making analysis of the bremsstruhlung
radiation from gas as well as from a W-target placed
into the relativistic plasma location. Figure 2
presents oscilloscope traces of such a flux at fixed
radius and shows that at the peak of the SGA regime
a copious amount of emission is detected, which is
obviously radiated by hot electrons colliding with
the target. Determined by this means the value of
the radius corresponds to the expected relativistic
Larmor radius, which only depends on the maximal
value of electron energy at a given value of the
pulse magnetic field strength. Moreover, the energy
of most of the energetic individual bremsstrahlung
photons from gas measured during amplitude
analysis equals the expected value of electron
energy at a given value of the pulse magnetic field
strength.
Values of density and average energy of
trapped electrons are obtained by integral
measurement and amplitude analysis from gas.
Experiments and numerical modeling of the process
showed that such a regime allowed to obtain dense
short lived electron bunches. Lifetime and densities
of the electron bunches were determined by initial
plasma parameters, microwave electric field
strength, velocity of magnetic field growth and
repetition rate of SGA-pulses. The measurement of
intensity of radiation from gas showed that its
maximum power is equal MeV/s106 4⋅ at rise time
of magnetic field 100 µs, relativistic plasma density
- 38 cm104 −⋅ ). The radiation power depends on the
rise time of pulse magnetic field – a shorter rise
time of magnetic field affects the SGA process by
better trapping condition for the electrons of initial
plasma.
Fig. 2. Oscillogramms of x-ray flashes
from the target (upper) and pulse
magnetic field (lower)
Obtained experimental and numerical simulation
data showed that time interval during which
relativistic bunches fell on a target strongly depends
on the rate of magnetic field decrease. Variation of
the repetition rate of SGA-pulses resulted in a
maximum value of bremsstruhlung intensity at
kHz10 f ≅ .
W-target insertion in relativistic plasma location
showed an increase of radiation intensity but only small
part of trapped particles falls on it. The intensity
strongly depends on location of the target and its size.
Insertion of the target inside the cavity deeper than 2.4
cm detunes the resonance.
3. Simulation of electron bunches generation
and their transportation on to a target
Simulation of SGA was carried out to investigate the
main problem of SGA – the problem of trapping of
plasma electrons in a regime of autoresonance
acceleration and to define the influence of SGA
parameters and parameters of initial plasma on trapping
conditions. Considering the conditions of experiments
3D-electrostatic model using particles has been applied
[4]. Equations for motion of plasma particles were
solved by means of leap-frog scheme [5]. The numerical
calculations provide information on 3D plasma
evolution, trap losses of particles, energy spectra of
electrons and ions, and plasma density that are beyond
the reach of both analytical methods and 2D simulation.
The aims of the simulation: a) to analyze space particles
distributions and electron energy spectra dependence on
initial conditions (initial plasma density and volume
occupied by plasma); b) to determine trapping
efficiency of electrons and losses particles from the trap.
To solve this problem a 3D electrostatic model with
the use of a CIC scheme is explored. Plasma heating
and confinement is simulated for a typical 2.4 GHz
plasma synchrotron.
Initially monoenergetic electrons (5 – 50 eV) and
ions (1eV) homogeneously distributed in space have
random directions of velocities. We simulated a
hydrogen plasma beam of densities of 310 cm10 −
axially injected into the cavity and confined in a mirror
trap (mirror ratio R=1.02). Microwave electric field
strength is taken 3 kV/cm. The velocity of magnetic
field growth in time provides average electron energy
increase 100 keV/µs. To satisfy requirements of a
particle in cell method 10 – 20 particles in a cell are
5
taken. Because of complexity of the problem under
investigation, schemes using Cartesian coordinates to
solve equations for particles motion as well as Poisson
equation have been used as the most cheapest and
developed. Equation of motion for each charged particle
in the form of Newton-Lorentz
×+++=
c
e
dt
d
indshf
BvEEEp
, (1)
where p and v are respectively the impulse and the
velocity of a charged particle, e is the electron charge,
Ehf is the microwave electric field strength, Es is the
self-consistent plasma electric field, Eind is the inductive
electric field, B is the superposition of magnetic fields
created by static magnetic coils and pulse magnetic
coils. Then a dimensionless centered finite difference
approximation of equation (1) after normalization to
ωcmo takes a form
n
nn
n
nn
buuguu ×++=
∆
− −+−+
γτ 2
2/12/12/12/1
,
(2)
where u is an impulse of the electron in cmo units, gn is
the total dimensionless electric field strength at time
moment n, bn is the normalized magnetic field value,
γ − relativistic factor , τ=ωt is dimensionless time, τ∆
is a time step. The equation (1) solved by a second-
order leap-frog Boris scheme [5]. For ions a
nonrelativistic equation is used. This is justified, as the
ions are not resonant particles.
The Poisson equation for periodic conditions
(influence of the cavity walls is supposed to be
neglected) is solved at each time step by using the
Boisvert code. Spatial limitation of plasma is accounted
for by assuming the particles reached the cavity walls to
be lost. Self-consistent electric field values are derived
from the obtained potential distribution on the mesh
with the use of finite difference derivatives. Electric
field values at points of particle locations are obtained
through inverse bilinear interpolation. Magnetic field
formed by static magnetic coils and pulse magnetic coils
is calculated at grid points. The use of particle in cell
method provides such an overwhelming spectrum of
time depended plasma parameters and characteristics
that one has to limit oneself just several of them. In the
proposed model the following diagnostics have been
applied:
1. Time dependence of losses for both sorts of
particles: electrons and ions.
2. Evolution of space distributions of electrons and
ions.
3. Time dependence of electron and ion energy
spectra.
Obtaining this data is enough to analyze collisionless
processes taking place in the phenomena of interest.
Cross-sections of space distribution of plasma
electrons after reaching average electron energy W=500
keV are presented in Fig. 3. Ions are not shown in the
figure. Calculation was made for initial plasma beam of
radius r0=4 mm, density 310
0 cm104 −⋅=n , electric
field strength E=3 kV/cm. It is seen from Fig.3 that as a
result of SGA a relativistic electron bunch is produced.
Total number of trapped electrons 10103 ⋅=trN .
Fig. 3. Cross-sections of spatial
distribution of electrons after SGA
pulse.
Dynamics of such a bunch can be controlled by
variation of magnetic field in time. A routine practice to
transport plasma electrons to a target is a magnetic field
decrease due to short-circuiting both pairs of magnetic
coils. Usually time of a magnetic field decrease is equal
to one of an increase. In this case the electron bunch
transforms to the electron ring. Interaction of the
electrons with the target lasts long enough but x – ray
power is rather low. To increase x – ray power a number
of approaches can be proposed. One of them – proposed
in the work – throwing a bunch on a target placed by the
side wall cavity or directly on to the cavity's side wall.
This is achieved after the short-circuiting one of pulse
magnetic coils when total magnetic field reaches its
maximum value. Another way is to add one more coil
producing reverse magnetic field. The removal of the
magnetic mirror results in appearance of the axial
magnetic gradient in the place where the electron bunch
is located. As a result a diamagnetic force
zz BF grad⋅−= µ (where µ is the magnetic moment of
the bunch which is proportional to the kinetic energy of
the electrons) acts on the bunch. Under action of the
diamagnetic force the bunch is pushed towards the
cavity's side wall. Simple estimate of an optimal value
-4 -2 0 2 4
-4
-2
0
2
4
accelerated
electron
bunch
target
Y,
c
m
Z, cm
-4 -2 0 2 4
-4
-2
0
2
4 target
electrons
nontrapped
bunch
electron
accelerated
Y,
c
m
X, cm
6
of axial gradient showed that for the above mentioned
parameters zBgrad should not exceed 8 G/cm.
However this estimate is valid just for static magnetic
field in case of a single particle approximation. That is
why optimal condition for the bunch transportation was
obtained from the analysis of simulation results. Time
of interaction of the bunch with the target and
consequently the power of x-ray depends on the velocity
of magnetic field decrease.
Fig.4. Time dependence of magnetic field
B(z,r) profile, r = 2 cm
Fig.5. Number of electrons has fallen on
the target at optimal
transportation condition
Figure 4 illustrates time dependence of a magnetic
field profile for r0=2 cm corresponding to the center of
the bunch for different time moments. Upper curve
corresponds to the end of SGA stage.
For different values of the velocity of the magnetic
field decrease one can obtain different times of
interaction of the bunch with the target At optimal
transportation condition bunch-target interaction time
can be less than 2 ns (Fig. 5).
Figure 5 presents a number of electrons falling on a
target at optimal transportation condition. It is seen from
this figure that interaction of the bunch with the target
lasts during just a few electron revolutions (several
nanoseconds). Taking into account that the bunch
contains 10101 ⋅ electrons at the energy of 0.5 MeV one
can obtain that at conversion rate 10% instantaneous
power of x-ray burst is about 16 kW. Such an
installation can acts with repetition rate up to 400 Hz.
One more way to rise x-ray power is the use of
the scheme with TE112 cavity (see Fig. 6). In this
case two electron bunches are produced as a result
of SGA. These bunches are confined in local
internal magnetic mirrors. After short-circuiting of
two internal coils internal magnetic mirrors are
removed. Then as a result of appearance of the
magnetic gradients in the places when electron
bunches are located both bunches are pushed to the
central plane of the system where they
simultaneously face the target and produce x-ray
burst (see Fig. 6). X-ray intensity increase by a
factor of two takes place in this case.
Fig. 6. Scheme of x-ray source with two
electron bunches. 1 – static
magnetic field coils; 2 – pulse
magnetic field coils; 3 – electron
bunches: 4 – target
Taking into consideration that the achievable
electron energy under SGA is determined by the
terminal value of the magnetic field and doesn't depend
on the microwave field strength one can obtain electron
bunches with energy of tens MeV (such a regime can be
possibly used for synchrotron radiation production).
However the density of trapped electrons does depend
on microwave field strength [3]. One more parameter
influencing both the density of electron bunches and
repetition rate of SGA cycles is the velocity of magnetic
field growth [6].
All things considered, one can estimate feasible
parameters of the electron bunch produced by SGA:
average energy of electrons 200 keV – 4.5 MeV,
volume 0.25 – 2.0 cm3, density 109 101 - 101 ⋅⋅ cm-3. As
for the typical x-ray burst it can range between 10 and
500 kilowatt during 2.0 – 50 ns. The repetition rate can
be as high as 400 Hz.
5. Conclusion
Obtained experimental and numerical modeling data
show that the most salient feature of SGA is the
possibility of obtaining Gyrac produced plasma or
electron bunches with parameters (average electron
energy, density and volume) which can be varied in
wide intervals. The SGA-regime can be used to obtain a
controlled bunch of relativistic electrons due to
variation of magnetic field in time. So the sphere of its
applications may be very wide. Interest to sources of
radiation on the basis of synchrotron gyromagnetic
autoresonance may be enhanced by the prospect of
7
designing a synchrotron radiation source as well as a
compact x-ray source for industrial application. Such a
source of intense hard x-ray can be used in atomic and
nuclear physics, defectoscopy, material processing,
medicine and biology.
6. References
1. K.S.Golovanivsky Autoresonance acceleration
of electrons at nonlinear ECR in a magnetic
field which is smoothly growing in time //
Physica Scripta. 1980, vol. 22, p. 126.
2. V.VAndreev., K.S.Golovanivsky. Plasma
synchrotron Gyrac-0 // Sov. Plasma Physics.
1985, vol. 11. p. 300.
3. V.VAndreev., A.M.Umnov Experiments with
relativistic plasma produced by a microwave
discharge in a time-dependent magnetic field //
Physica Scripta. 1991, vol. 43. p. 490.
4. R.W.Hockney, J.W.Eastwood Computer.
simulation using particles // 1981. McGraw-Hill
Inc.
5. A.B.Langdon, F. Lazinsky. Relativistic and
electromagnetic models // Methods in Comput.
Phys., Controlled Fusion 1976, vol. 16, p. 347.
6. V.VAndreev., A.M.Umnov A.M. Gyrac-D-0
Relativistic plasma accumulator and ion
accelerator // Rev. Sci. Instr. 1992, Vol. 63, p.
2907.
7. V.VAndreev., A.M.Umnov Gyrac-D-0
Relativistic plasma and electron bunches in
plasma synchrotron of GYRAC // Plasma
Sources Sci. Technol., 1999, vol. 8, p. 479.
2. Experimental device
5. Conclusion
|