Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB)
In the present paper the results from theoretical and experimental studies as well as from 2.5-D numerical simulation of both the plasma WF excitation by either REB or LP and the CPWF acceleration are discussed. The results of these investigations make it possible to evaluate the potentialities of t...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) / V.A. Balakirev, I.V. Karas’, V.I. Karas’, V.D. Levchenko, M. Bornatici // Вопросы атомной науки и техники. — 2003. — № 4. — С. 29-32. — Бібліогр.: 14 назв. — англ. |
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Balakirev, V.A Karas, I.V. Karas’, V.I. Levchenko, V.D. Bornatici, M. 2017-01-07T16:49:39Z 2017-01-07T16:49:39Z 2003 Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) / V.A. Balakirev, I.V. Karas’, V.I. Karas’, V.D. Levchenko, M. Bornatici // Вопросы атомной науки и техники. — 2003. — № 4. — С. 29-32. — Бібліогр.: 14 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/111001 533.9 In the present paper the results from theoretical and experimental studies as well as from 2.5-D numerical simulation of both the plasma WF excitation by either REB or LP and the CPWF acceleration are discussed. The results of these investigations make it possible to evaluate the potentialities of the WF acceleration method and to analyse whether it can serve as basis for creating a new generation of devices capable of accelerating CP at substantially higher (by two to three orders of magnitude) rates in comparison with those achievable in classical linear high-frequency (resonant) accelerators. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые методы ускорения заряженных частиц Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) |
| spellingShingle |
Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) Balakirev, V.A Karas, I.V. Karas’, V.I. Levchenko, V.D. Bornatici, M. Новые методы ускорения заряженных частиц |
| title_short |
Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) |
| title_full |
Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) |
| title_fullStr |
Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) |
| title_full_unstemmed |
Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) |
| title_sort |
charged particle (cp) acceleration by an intense wake-field (wf) excited in plasmas by either laser pulse (lp) or relativistic electron bunch (reb) |
| author |
Balakirev, V.A Karas, I.V. Karas’, V.I. Levchenko, V.D. Bornatici, M. |
| author_facet |
Balakirev, V.A Karas, I.V. Karas’, V.I. Levchenko, V.D. Bornatici, M. |
| topic |
Новые методы ускорения заряженных частиц |
| topic_facet |
Новые методы ускорения заряженных частиц |
| publishDate |
2003 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| description |
In the present paper the results from theoretical and experimental studies as well as from 2.5-D numerical simulation of both the plasma WF excitation by either REB or LP and the CPWF acceleration are discussed. The results of these investigations make it possible to evaluate the potentialities of the WF acceleration method and to analyse whether it can serve as basis for creating a new generation of devices capable of accelerating CP at substantially higher (by two to three orders of magnitude) rates in comparison with those achievable in classical linear high-frequency (resonant) accelerators.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111001 |
| citation_txt |
Charged particle (CP) acceleration by an intense wake-field (WF) excited in plasmas by either laser pulse (LP) or relativistic electron bunch (REB) / V.A. Balakirev, I.V. Karas’, V.I. Karas’, V.D. Levchenko, M. Bornatici // Вопросы атомной науки и техники. — 2003. — № 4. — С. 29-32. — Бібліогр.: 14 назв. — англ. |
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2025-11-25T06:31:29Z |
| last_indexed |
2025-11-25T06:31:29Z |
| _version_ |
1850509545244196864 |
| fulltext |
UDC 533.9
CHARGED PARTICLE (CP) ACCELERATION BY AN INTENSE WAKE-
FIELD (WF) EXCITED IN PLASMAS BY EITHER LASER PULSE (LP)
OR RELATIVISTIC ELECTRON BUNCH (REB)
V.A.Balakirev, I.V.Karas’, V.I.Karas’, V.D.Levchenko*, M.Bornatici**
NSC “Kharkov Institute of Physics & Technology”, Kharkov, Ukraine, karas@kipt.kharkov.ua
*Keldysh Institute of Applied Mathematics of RAS, Moscow, Russia, lev@KELDYSH.ru
**INFM, Dipartimento di Fisica “A. Volta”, Università degli Studi di Pavia, Pavia, Italy, bor-
natici@fisicavolta.unipv.it
In the present paper the results from theoretical and experimental studies as well as from 2.5-D numerical simu-
lation of both the plasma WF excitation by either REB or LP and the CPWF acceleration are discussed. The results
of these investigations make it possible to evaluate the potentialities of the WF acceleration method and to analyse
whether it can serve as basis for creating a new generation of devices capable of accelerating CP at substantially
higher (by two to three orders of magnitude) rates in comparison with those achievable in classical linear high-fre-
quency (resonant) accelerators.
Collective methods of CP acceleration were pro-
posed by Budker [1], Veksler [2], Fainberg [3]. Budker
[1] proposed the CP acceleration in self–stabilized rela-
tivistic electron beam; Veksler [2] suggested the method
of ion coherent acceleration by relativistic electron ring
in longitudinally varying magnetic field; Fainberg [3]
proposed the plasma–based scheme for CP acceleration
by space-charge waves in plasma and non-compensated
beams. At present this is one of the most promising
methods for collective acceleration because the electric
field amplitude of the space–charge wave (SCW) in a
plasma attains a maximum value
2 1/ 2 1/ 2
max 0 0/ (4 ) (2 1)pE n n n mcπ γ= − (1)
(formula extended [4] to relativistic case) m is the elec-
tron mass; c is the light speed; γ is the relativistic fac-
tor; np is the maximum density in the SCW; the ratio
np/n0 is governed by the way in which the SCW is initi-
ated. Since very large perturbations of the charge densi-
ty (attaining the value of the unperturbed plasma density
0n ) can be obtained, the accelerating fields can reach
values of 107-109 V/cm.
The efficient methods for plasma wave excitation:
-PWGA–plasma waveguide accelerator–a) electron
beam–plasma interaction in magnetized plasma waveg-
uide (beam – plasma instability); b) external ultra-high
oscillator – Y.B. Fainberg and co-workers (since 1956);
-PBWA–plasma beat–wave accelerator–f1–f2 =fp (fi
is the radiation frequency, fp is the Langmuir frequency)
Tajima and Dawson (1979 a detailed information con-
cerning this and next references you can you see in [5]);
in BWA, an electric field of 1.8x109 V/cm and energy of
accelerated particles of 20 MeV were obtained C. Clay-
ton, C. Joshi, C. Darrow, K.A. Marsh, A. Dyson M. Ev-
erett, A. Lai, W.P. Leemans, D.Umstadter, R. Williams,
Y. Kitagava, T. Matsumoto, T. Minamihata, K. Sawai,
K. Matsuo, K. Mima, K. Nishihara, H. Azechi,
K.A. Tanaka, H. Takabe, and S. Nakai (1992,1993);
-SmLWFA-self–modulated laser wake–field accel-
erator self-modulation of laser pulse N.E. Andreev et al
(1992); J. Krall et al (1993); T.M. Antonsen, P. Mora
(1992); P Sprangle et al (1992); The most impressive re-
sults on plasma acceleration of CP were obtained in the
SmLWFA, i.e. an electric field amplitude of 1.5-
2x108 V/cm, an energy of accelerated particles of 100-
300 MeV K. Nakajima et al. (1994); A. Modena, Z. Na-
jmudin, A.E Dangor et al(1995); D. Umstadter, J.K.
Kim, E. Dodd (1996). The extremely large acceleration
gradients generated by laser pulses propagating in plas-
mas can be used to accelerate electrons. In the standard
LWFA a short laser pulse, on the order of a plasma
wavelength long, excites a trailing plasma wave that can
trap and accelerate electrons to high energy. There are a
number of issues that must be resolved before a viable,
practical high energy accelerator can be developed.
These include Raman, modulation and hose instabilities
that can disrupt the acceleration process. In addition, ex-
tended propagation of the laser pulse is necessary to
achieve high-electron energy. In the absence of optical
guiding the acceleration distance is limited to a few
Rayleigh ranges, which is far below that necessary to
reach GeV electron energies.
-LPSh-laser pulse shaping S.V. Bulanov,
T.J. Esirkepov, N.M. Naumova, F. Pegoraro,
I. Pogorel’sky A.M. Pukhov (1996);
-RLPA-resonant laser-plasma accelerator – train of
laser pulses with independenly adjustable pulse widths
and interpulse spacing S. Dalla, M. Lontano (1994); D.
Umstadter, E. Esarey, J. Kim (1994);
-LWFA–laser wake–fields accelerator – the short
laser pulse T. Tajima, J.M. Dawson (1979); L.M. Gor-
bunov, V.I. Kirsanov (1987); for relativistic strong pulse
S.V. Bulanov et al. (1989); P. Sprangle et al. (1990). To
achieve multi GeV electron energies in the laser wake-
field accelerator, it is necessary to propagate an intense
laser pulse over long distances in a plasma without dis-
ruption. The physics of laser beams propagating in plas-
mas has been studied in great detail and there exists
sample experimental confirmation of extended guided
propagation in plasmas and plasma channels. In addition
to these issues, dephasing of electrons in the wakefield
can limit the energy gain. Spatially tapering the plasma
density may be useful for overcoming electron dephas-
ing in the wake-field. P. Sprangle, J.R. Penàno, B.
Hafizi, R.F. Hubbard, A. Ting, D.F. Gordon, A. Zigler,
mailto:bornatici@fisicavolta.unipv.it
mailto:bornatici@fisicavolta.unipv.it
mailto:irina@KELDYSH.ru
mailto:karas@kipt.kharkov.ua
T.M. Antonsen, Jr. (2000-2002) proposed and studied
guiding and stability of an intense laser pulse in a uni-
form plasma channel and analyzed the WF acceleration
process in an inhomogeneous channel. The coupled
electromagnetic and plasma wave equations were de-
rived for laser pulses propagating in a plasma channel
with a parabolic radial density profile and arbitrary axial
density variation. For a uniform channel, Raman and
modulation instabilities were analyzed. For a nonuni-
form channel the axial and radial electric fields associat-
ed with the plasma wave were obtained inside and be-
hind the laser pulse. It was shown that by optimally ta-
pering the plasma density the WF phase velocity several
plasma wavelengths behind the laser pulse can be equal
the speed of light in vacuum. A three-dimensional enve-
lope equation for the laser field has been derived that in-
cludes nonparaxial effects, WF, and relativistic nonlin-
earities. In the broad beam, short pulse limit the nonlin-
ear terms in the wave equation that lead to Raman and
modulation instabilities cancel. Long pulses (several
plasma pλ wave lengths) experience substantial modi-
fication due to these instabilities. The short pulse
LWFA, although having smaller accelerating fields, can
provide acceleration for longer distances in a plasma
channel. By allowing the plasma density to increase
along the propagation path electron dephasing can be
deferred, increasing the energy gain. A simulation ex-
ample of a GeV channel guided LWFA accelerator is
presented. Simulations also show [6] that multi-GeV en-
ergies can be achieved by optimally tapering the plasma
channel.
-PWFA–plasma wake–fields accelerator – the short
rectangular REB or periodic train of REBs P. Chen,
J.M. Dawson, R.M.Huff and T.Katsouleas; Blow out
regime of PWFA J. B.Rosenzweig et al. (1991). In the-
PWFA, an electric field of 6x104 V/cm and energy of
accelerated particles of 6 MeV (can see in [5] reference
J.Rosenzweig, D.Cline, B.Cole et al. (1988)); in blow
out regime of PWFA, energy gradients of 700 Mev/m
were measured in the experiment E–157 S. Lee, T. Kat-
souleas, P. Muggli, W. Mori, C.Joshi, R.Hemker, E.S.-
Dodd, C.E.Clayton, K.Marsh et al. (2000); project “En-
ergy doubler for a linear collider” S. Lee, T. Katsouleas,
P.Muggli, W. Mori, C. Joshi, R. Hemker, E.S. Dodd,
C.E. Clayton, K. Marsh et al. (2002) [7]. An intense,
high-energy electron or positron beam can have focused
intensities rivaling those of today’s most powerful laser
beams. For example, the 5 ps (full-width, half-maxi-
mum), 50 GeV beam at the Stanford Linear Accelerator
Center (SLAC) at 1 kA and focused to a 3 micron rms
spot size yields intensities of 1020 W/cm2 at a repetition
rate of 10 Hz. Unlike a ps or fs laser pulse which inter-
acts with the surface of a solid target, the particle beam
can readily tunnel through tens of cm of steel. However,
as it is shown in [7] the same particle beam can be ma-
nipulated quite effectively by the plasma that is a mil-
lion times less dense than air! This is because of the
very strong collective fields induced in the plasma by
the Coulomb force of the beam. The collective fields in
turn react back onto the beam leading to many clearly
observable phenomena. The beam particles can be: 1)
deflected leading to focusing, defocusing, or even steer-
ing of the beam; 2) undulated causing the emission of
spontaneous betatron x-ray radiation; 3) accelerated or
decelerated by the plasma fields. Using the 28.5 GeV
electron beam from the SLAC linac a series of experi-
ments have been carried out that demonstrated clearly
many of the above mentioned effects [7]. The results
were compared with theoretical predictions and with
two-dimensional and three-dimensional, one-to-one,
particle-in-cell code simulations [7]. These phenomena
may have practical applications in future technologies
including optical elements in particle beam lines, syn-
chrotron light sources, and ultrahigh gradient accelera-
tors. As can be seen from spatial distribution of excited
WF [7], the electric field can attain high values only
over very short distances. Therefore we think that the
energy doubler for a linear SLAC collider problem is
not very realistic.
An interesting result has been established by us [5]:
for a certain relation among the parameters of the plas-
ma – bunch – magnetic field system, the hybrid nature
of the wake waves (which are excited by a REB in a
magnetized plasma and are a superposition of the sur-
face and spatial modes) makes it possible to increase the
electron energy (EE) of the accelerated bunch to a value
that is significantly higher than the initial EE of the ac-
celerating bunch (even when the bunch is initially un-
modulated in the longitudinal direction). We have dis-
cussed 2.5-dimensional numerical modeling on the for-
mation of an ion channel as a result of the radial ion mo-
tion in self-consistent electromagnetic fields excited by
a train of REB. The parameters of the fully developed
channel are determined by the plasma-to-bunch density
ratio and the ratio of the bunch radius to the skin depth.
The effective dimensions of the channel and its “depth”
(i.e., the high ion density at the channel axis) increase
monotonically both in time and in the direction opposite
to the propagation direction of the bunches. The formed
ion channel stabilizes the propagation of REB, which
thus generate stronger accelerating fields. The results of
the wake-field excitation during the self-modulation of a
long REB has shown that the maximum electron density
in the bunch becomes comparable to the plasma density
and the amplitude of the plasma density perturbations
becomes larger than the initial plasma density by a fac-
tor of 4.5. This indicates a very strong modulation of
both the bunch density and the plasma density. That is
why, even in the above case of a low-density bunch (in
which the unperturbed electron density is about two or-
ders of magnitude lower than the plasma density), it is
incorrect to describe the plasma in the linear approxima-
tion. The amplitude of the longitudinal field is about 0.8
of the maximum electric field that can be generated in
the plasma, and the amplitude of the radial field is about
0.4 of the maximum possible field. This shows that the
driven bunch needs to be placed in the acceleration sta-
bility region. An important point is that the field ampli-
tude increases only over a certain distance along a REB;
hence, it would be of no use to operate with bunches
whose length exceeds the distance over which the longi-
tudinal field amplitude is maximum, because doing so
would provide no additional increase in the excited
wake field. The results obtained with allowance for all
possible nonlinearities give a better insight into the three
-dimensional behaviour of REB in a plasma and may
help to ensure the optimum conditions for the wake –
field generation during the dynamic self-modulation of
the bunches. The results of investigations of the excita-
tion of accelerating fields by an individual REB or by a
train of such bunches in a plasma (in particular, in the
presence of an external magnetic field) make it possible
to evaluate the potentialities of the wake-field accelera-
tion method.
Further more, we discuss the physical mechanism
for generation of very high “quasi-static” magnetic
fields in the interaction of an ultraintense short laser
pulse with an overdense plasma target owing to the spa-
tial gradients and non-stationary character of the pon-
deromotive force. Numerical (particle-in-cell) simula-
tions by Wilks et al. [8] of the interaction of an ultrain-
tense laser pulse with an overdense plasma target have
revealed nonoscillatory self-generated magnetic fields
up to 250MG in the overdense plasma, that this non-os-
cillatory magnetic field is generated around the heated
spot in the center of the plasma, the magnetic field gen-
eration being attributed to the electron heating at the ra-
diation-plasma interface. The spatial and temporal evo-
lution of spontaneous megagauss magnetic fields, gen-
erated during the interaction of a picosecond pulse with
solid targets at irradiances above 5 x 1018 W/cm2 have
been measured using Faraday rotation with picosecond
resolution, the observations being limited to the region
of underdense plasma and after a laser pulse [9]. A high
density plasma jet has been observed simultaneously
with the magnetic fields by interferometry and optical
emission and a field value is consistent with field gener-
ated by the thermoelectric mechanism (see for example
[10]). In paper [11] the first direct measurements of
high-energy proton generation (up to 18 MeV) and
propagation into a solid target during such intense (5 x
1019 W/cm2) laser plasma interactions were reported.
Measurements of the deflection of these energetic pro-
tons were carried out which imply that magnetic fields
in excess of 30 MG exist inside the target. In [12] we
solved numerically the problem of high-intensity, lin-
early polarized electromagnetic pulse incident onto a
collisionless plasma layer in a Cartesian coordinate sys-
tem in a 2.5-D formulation (z is the cyclic coordinate
and there are three components of the momentum) by
means of COMPASS (COMputer Plasma And Surface
Simulation) code. The recent review [5] and references
therein combine a detailed information concerning
COMPASS code as well as its possibilities and applica-
tions. A general advantage of the complete numerical
simulation consists of the possibility of obtaining all
necessary information concerning spatial and temporal
dynamics of both particles and self-consistent electro-
magnetic fields without requiring additional data (re-
flection and absorption coefficients, changes of either
plasma temperature or different plasma parameters) for
a given situation concerning the interaction of an inten-
sive electromagnetic pulse with plasmas. We give only
the external parameters, both the initial and boundary
conditions for particles and fields, and as results of a nu-
merical simulation we attain all characterictics of the
plasma together with pulsed self-consistent electromag-
netic fields. The most characteristic feature of the action
of an intense, normally incident electromagnetic pulse
onto an ultrahigh-density plasma consists in a “well-dig-
ging” effect. Worth nothing is the time-growing sharp
nonuniformity of the perturbed plasma layer in the
transverse direction. As for the magnetic field, we do
not observe a change of its direction, but a significant
time-variation of its strength varies significantly in time.
Hence, the magnetic field cannot be considered as
quasi-static because it varies by more than an order of
magnitude over a time of
12 −
peπ ω . The magnitude of
the “dc” magnetic field is ten times as low as the maxi-
mum magnetic field. One should note that in [8, 12] the
numerical simulation has been made under very optimal
conditions: a uniform plasma density makes it sure a
own plasma oscillation resonance with a longitudinal
modulation density of particles in a wave as well as a
maximum frequency of nonlinear Tomson scattering
spectrum. In experiments, instead, a plasma inhomo-
geneity is very essential, with the result that resonant
conditions are fulfilled only in a small plasma region.
Subsequently to the interaction pulse, only the “dc”
magnetic field exists, as measured in the underdense
plasma region in [9]. On the basis of the formula:
)(/))/(10(2.4)( 2/1222 mmWIxMGBdc µλ−= (2)
(where I is the intensity of the incident laser radiation)
one obtains a “dc” magnetic field magnitude of few MG
for the experimental parameters of [9], and a few tens of
MG for the experimental conditions of [11]. A differ-
ence still on order of value is conditioned that at such
intensities only 10% of the incident laser radiation is ab-
sorbed in agreement with [13]. By means of a 2.5-di-
mensional numerical simulation on the macroparticles
method it is possible to find the magnetic field spatial
and temporal distribution without making use of an
adapted parameter, in contrast with the conventional
Tnx∇∇ mechanism (see for example [10]). On the
other hand, the theoretical model for the generation of a
magnetic field proposed by Sudan [14] does not appear
to be appropriate, this model being valid for a very large
ratio of plasma density to critical density and when the
Tnx∇∇ contribution is not relevant.
The work was supported in part by the Cariplo
Foundation (Como, Italy) and INTAS project # 01-233.
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14. R.N. Sudan, // Phys. Rev. Lett., 1993, 20, 307
Further more, we discuss the physical mechanism for generation of very high “quasi-static” magnetic fields in the interaction of an ultraintense short laser pulse with an overdense plasma target owing to the spatial gradients and non-stationary character of the ponderomotive force. Numerical (particle-in-cell) simulations by Wilks et al. [8] of the interaction of an ultraintense laser pulse with an overdense plasma target have revealed nonoscillatory self-generated magnetic fields up to 250MG in the overdense plasma, that this non-oscillatory magnetic field is generated around the heated spot in the center of the plasma, the magnetic field generation being attributed to the electron heating at the radiation-plasma interface. The spatial and temporal evolution of spontaneous megagauss magnetic fields, generated during the interaction of a picosecond pulse with solid targets at irradiances above 5 x 1018 W/cm2 have been measured using Faraday rotation with picosecond resolution, the observations being limited to the region of underdense plasma and after a laser pulse [9]. A high density plasma jet has been observed simultaneously with the magnetic fields by interferometry and optical emission and a field value is consistent with field generated by the thermoelectric mechanism (see for example [10]). In paper [11] the first direct measurements of high-energy proton generation (up to 18 MeV) and propagation into a solid target during such intense (5 x 1019 W/cm2) laser plasma interactions were reported. Measurements of the deflection of these energetic protons were carried out which imply that magnetic fields in excess of 30 MG exist inside the target. In [12] we solved numerically the problem of high-intensity, linearly polarized electromagnetic pulse incident onto a collisionless plasma layer in a Cartesian coordinate system in a 2.5-D formulation (z is the cyclic coordinate and there are three components of the momentum) by means of COMPASS (COMputer Plasma And Surface Simulation) code. The recent review [5] and references therein combine a detailed information concerning COMPASS code as well as its possibilities and applications. A general advantage of the complete numerical simulation consists of the possibility of obtaining all necessary information concerning spatial and temporal dynamics of both particles and self-consistent electromagnetic fields without requiring additional data (reflection and absorption coefficients, changes of either plasma temperature or different plasma parameters) for a given situation concerning the interaction of an intensive electromagnetic pulse with plasmas. We give only the external parameters, both the initial and boundary conditions for particles and fields, and as results of a numerical simulation we attain all characterictics of the plasma together with pulsed self-consistent electromagnetic fields. The most characteristic feature of the action of an intense, normally incident electromagnetic pulse onto an ultrahigh-density plasma consists in a “well-digging” effect. Worth nothing is the time-growing sharp nonuniformity of the perturbed plasma layer in the transverse direction. As for the magnetic field, we do not observe a change of its direction, but a significant time-variation of its strength varies significantly in time. Hence, the magnetic field cannot be considered as quasi-static because it varies by more than an order of magnitude over a time of . The magnitude of the “dc” magnetic field is ten times as low as the maximum magnetic field. One should note that in [8, 12] the numerical simulation has been made under very optimal conditions: a uniform plasma density makes it sure a own plasma oscillation resonance with a longitudinal modulation density of particles in a wave as well as a maximum frequency of nonlinear Tomson scattering spectrum. In experiments, instead, a plasma inhomogeneity is very essential, with the result that resonant conditions are fulfilled only in a small plasma region. Subsequently to the interaction pulse, only the “dc” magnetic field exists, as measured in the underdense plasma region in [9]. On the basis of the formula:
(2)
(where I is the intensity of the incident laser radiation) one obtains a “dc” magnetic field magnitude of few MG for the experimental parameters of [9], and a few tens of MG for the experimental conditions of [11]. A difference still on order of value is conditioned that at such intensities only 10% of the incident laser radiation is absorbed in agreement with [13]. By means of a 2.5-dimensional numerical simulation on the macroparticles method it is possible to find the magnetic field spatial and temporal distribution without making use of an adapted parameter, in contrast with the conventional mechanism (see for example [10]). On the other hand, the theoretical model for the generation of a magnetic field proposed by Sudan [14] does not appear to be appropriate, this model being valid for a very large ratio of plasma density to critical density and when the contribution is not relevant.
The work was supported in part by the Cariplo Foundation (Como, Italy) and INTAS project # 01-233.
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