On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target
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 usage an adapted parameter unlike of the conventional ◊nx◊ T mechanism. On the other hand, theoretical model for the generation of a m...
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| Цитувати: | On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target / V.I. Karas’, O.V. Batishchev, M. Bornatici // Вопросы атомной науки и техники. — 2003. — № 4. — С. 143-147. — Бібліогр.: 32 назв. — англ. |
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Karas’, V.I. Batishchev, O.V. Bornatici, M. 2017-01-08T17:14:11Z 2017-01-08T17:14:11Z 2003 On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target / V.I. Karas’, O.V. Batishchev, M. Bornatici // Вопросы атомной науки и техники. — 2003. — № 4. — С. 143-147. — Бібліогр.: 32 назв. — англ. 1562-6016 PACS: 52.40.Nk, 52.65.Kj, 52.70.Ds, 52.70. Kz https://nasplib.isofts.kiev.ua/handle/123456789/111177 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 usage an adapted parameter unlike of the conventional ◊nx◊ T mechanism. On the other hand, theoretical model for the generation of a magnetic field proposed by R. Sudan is not appropriate, this model being very large ratio of plasma density to critical density and when the ◊nx◊ Tcontribution is not relevant. The work by V.I. Karas` was supported in part by the Cariplo Foundation (Como, Italy) and INTAS project #01-233. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Нелинейные процессы On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target Article published earlier |
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On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target |
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On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target Karas’, V.I. Batishchev, O.V. Bornatici, M. Нелинейные процессы |
| title_short |
On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target |
| title_full |
On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target |
| title_fullStr |
On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target |
| title_full_unstemmed |
On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target |
| title_sort |
on the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target |
| author |
Karas’, V.I. Batishchev, O.V. Bornatici, M. |
| author_facet |
Karas’, V.I. Batishchev, O.V. Bornatici, M. |
| topic |
Нелинейные процессы |
| topic_facet |
Нелинейные процессы |
| publishDate |
2003 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| description |
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 usage an adapted parameter unlike of the conventional ◊nx◊ T mechanism. On the other hand, theoretical model for the generation of a magnetic field proposed by R. Sudan is not appropriate, this model being very large ratio of plasma density to critical density and when the ◊nx◊ Tcontribution is not relevant.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111177 |
| citation_txt |
On the mechanisms of strong magnetic field excitation at the interaction of ultraintense short laser pulse with an plasma target / V.I. Karas’, O.V. Batishchev, M. Bornatici // Вопросы атомной науки и техники. — 2003. — № 4. — С. 143-147. — Бібліогр.: 32 назв. — англ. |
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2025-11-26T09:50:39Z |
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2025-11-26T09:50:39Z |
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| fulltext |
ON THE MECHANISMS OF STRONG MAGNETIC FIELD EXCITATION
AT THE INTERACTION OF ULTRAINTENSE SHORT LASER PULSE
WITH AN PLASMA TARGET
V.I. Karas’a, O.V. Batishchev b, M. Bornatici c
aNSC “Kharkov Institute of Physics & Technology”, Kharkov, Ukraine, karas@kip-
t.kharkov.ua;
bMIT Plasma Fusion Center, Cambridge, Massachusetts 02139, USA;
cINFM, Dipartimento di Fisica “A. Volta”, Università degli Studi di Pavia, Pavia 27100, Italy
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 usage an adapted parameter unlike of the conventional
Tnx∇∇ mechanism. On the other hand, theoretical model for the generation of a magnetic field proposed by
R. Sudan is not appropriate, this model being very large ratio of plasma density to critical density and when the
Tnx∇∇ contribution is not relevant.
PACS: 52.40.Nk, 52.65.Kj, 52.70.Ds, 52.70. Kz
1. INTRODUCTION
The interaction between intense laser radiation and
matter is known to produce a wealth of nonlinear ef-
fects. Those include fast electron and ion generation [1–
5] indicating that ultra-strong electric fields are pro-
duced in the course of the laser–plasma interaction. An
equally ubiquitous, although less studied, effect accom-
panying laser–matter interaction is the generation of ul-
tra-strong magnetic fields in the plasma [6–11]. Magnet-
ic fields can have a significant effect on the overall non-
linear plasma dynamics. Extremely high (few mega-
gauss) azimuthal magnetic fields play an essential role
in the particle transport, propagation of laser pulses,
laser beam self-focusing, penetration of laser radiation
into the overdense plasma and the plasma electron and
ion acceleration.
2. INVERSE FARADAY EFFECT
The generation of an axial magnetic field in the plas-
ma by a circularly (or elliptically) polarized laser is of-
ten referred to as the inverse Faraday effect (IFE). First
theoretically described by Pitaevskii [12] and Steiger
and Woods [13] it results from the features of the elec-
tron motion in a circularly polarized electromagnetic
wave. During the interaction of the plasma electrons
with the circularly polarized laser pulse, electrons ab-
sorb both the laser energy and the angular momentum of
the laser pulse. In particular, the angular momentum ab-
sorption leads to the electron rotation and generation of
the axial magnetic field by the azimuthal electron cur-
rent. Naturally, IFE does not occur for a linearly polar-
ized laser pulse since it does not possess any angular
momentum. IFE has since been measured in several ex-
periments [9,14, 15]. The conditions under which IFE is
possible are still not fully explored. What is theoretical-
ly known [16] is that there is no magnetic-field genera-
tion during the interaction of the inhomogeneous circu-
larly polarized electromagnetic waves with the homoge-
neous plasma. Magnetic field can be produced in the
presence the strong plasma inhomogeneity [17–19] ei-
ther preformed or developed self-consistently during the
interaction. More recently a mechanism has been pro-
posed for the generation of an axial magnetic field
through the transfer of the spin of the photons during the
absorption of a transversely nonuniform circularly po-
larized radiation [20]. The magnetic field thus generated
has a magnitude proportional to the transverse gradient
of the absorbed intensity and inverse proportional to the
electron density, the latter sealing being in contrast to
earlier theories of IFE [20]. Along the same lines as
[20], it has been demonstrated that in laser-plasma inter-
actions strong axial magnetic fields can be generated
through angular (spin) momentum absorption by either
electron-ion collisions or ionization. Yet another mecha-
nism of magnetic field generation has been proposed (in
framework of classical electrodynamics) [21], based on
the resonant absorption by energetic electrons of a cir-
cularly polarized laser pulse. The resonance occurs be-
tween the fast electrons, executing transverse (betatron)
oscillations in a fully or partially evacuated plasma
channel, and the electric field of the laser pulse. The be-
tatron oscillations are caused by the action of the elec-
trostatic force of the channel ions and self-generated
magnetic field. This type of resonant interaction was re-
cently suggested as a mechanism for accelerating elec-
trons to highly relativistic energies [21,22]. When a cir-
cularly polarized laser pulse is employed, its angular
momentum can be transferred to fast resonant electrons
along with its energy. The resulting electron beam spi-
rals around the direction of the laser propagation, gener-
ating the axial magnetic field [21]. In [21] the intensity
of the magnetic field generated in relativistic laser chan-
nel was calculated taking into ac-count self-generated
static fields, which are neglected in known IFE theories
[17–19]. Calculations [21] are in agreement with the re-
cent experiments at the Rutherford Appleton Laboratory
(RAL) [15] which exhibited very large (several mega-
gauss) axial magnetic fields during the propagation of a
sub-picosecond laser pulse in a tenuous plasma. The rel-
evant aspect of the RAL experiment is that both fast
electrons and the strong magnetic field were measured
in the same experiment.
3. MAGNETIC FIELD EXCITATION IN UN-
DERDENSE PLASMA
In an underdense longitudinal inhomogeneous plas-
ma the nonrelativistic two-dimensional treatment of
self-generated magnetic fields was presented in the arti-
cle [23], showing that a laser beam propagating along a
density plasma gradient produces a rotational current
which gives rise to a quasi-static magnetic field. An
analogous mechanism was considered earlier in the pa-
per [24] whereas the nonlinear mixing of two electro-
magnetic waves in a nonuniform plasma was discussed
in the work [25]. They investigated a circularly polar-
ized pulse for which the generation of low-frequency
electromagnetic field is due to the inverse Faraday ef-
fect. In the extremely strong relativistic regime the mag-
netic field generated by the laser beams in underdense
plasma was recently studied numerically [26]. The main
objective of the work [18] was to investigate self-gener-
ated quasi-static magnetic fields both in the laser pulse
body and behind the pulse in the region of the wake-
field. Authors treated the laser radiation as linearly po-
larized and the plasma as uniform and underdense. The
analytical work was based on a perturbation theory ap-
plied to the set of relativistic cold electron fluid equa-
tions and Maxwell’s equations. The quasi-static magnet-
ic field generated by a short laser pulse in a uniform rar-
efied plasma is found analytically and compared to two-
dimensional particle-in-cell simulations .It is shown that
a self-generation of quasi-static magnetic fields takes
place in fourth order with respect to the parameter vE/c
where vE and c are the electron quiver velocity and the
light speed, respectively. In the wake region the magnet-
ic field possesses a component which is homogeneous
in the longitudinal direction and is due to the steady cur-
rent produced by the plasma wakefield and a component
which is oscillating at the wave number 2kp,, where kp is
the wave number of the plasma wake, a known property
of nonlinear plasma waves [27,28]. Numerical particle
simulations confirm the analytical results and are also
used to treat the case of high intense laser pulses with
vE/c >1. The resultant magnetic field has a focusing ef-
fect on relativistic electrons in the plasma wakefield ac-
celerator context.
4. MAGNETIC FIELD EXCITATION IN
OVERDENSE PLASMA
Further we discuss the physical mechanism for gen-
eration 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. [10] of the interaction of an ultraintense
laser pulse with an overdense plasma target have re-
vealed non-oscillatory self-generated magnetic fields up
to 250 MG in the overdense plasma, that this nonoscilla-
tory magnetic field around the heated spot in the center
of the plasma, the magnetic field generation being at-
tributed to the electron heating at the radiation-plasma
interface. The spatial and temporal evolution of sponta-
neous megagauss magnetic fields, generated during the
interaction of a picosecond pulse with solid targets at ir-
radiances above 5 x 1018 W/cm2 have been measured us-
ing Faraday rotation with picosecond resolution, the ob-
servations being limited to the region of underdense
plasma and after a laser pulse Fig.1, [6]. A high density
plasma jet has been observed simultaneously with the
magnetic fields by interferometry and optical emission.
Fig.1. Magnetic field distribution extracted from the po-
larigram. The magnitude is in units of megagauss. The
plasma region either obscured by selfemission or not
accessible for probing is shown, (from [6])
Because of the high temporal resolution of the probe
diagnostic, a quantitative measurement of the transient
nature of the fields has been obtained for the first time.
Interestingly, no Faraday rotation was detected immedi-
ately after the interaction, a possible reason being that
the fields were still limited to regions not accessible for
probing. After 5 ps the typical signatures corresponding
to a toroidal field surrounding the laser axis (i.e., a dark
and a bright pattern on opposing sides of the axis, in the
proximity of the target surface) began to appear. The
strongest rotations were detected between 6 and 12 ps
after the interaction. As expected, the dark-bright pat-
tern reverses as the angle between the polarizers is
changed from a value below 90° to a value above 90°.
The sense of rotation is the same as observed in previ-
ous measurements in longer pulse regimes and is consis-
tent with fields generated by the thermoelectric mecha-
nism (see for example [30]). In paper [7a] the first direct
measurements of high energy proton generation (up to
18 MeV) and propagation into a solid target during such
intense laser plasma interactions were reported. Mea-
surements of the deflection of these energetic protons
were carried out which imply that magnetic fields in ex-
cess of 30 MG exist inside the target. The structure of
these fields is consistent with those produced by a beam
of hot electrons which has also been measured in these
experiments. The intensity on target of laser radiation
was up to 5×1019 W/cm2 and was determined by simul-
taneous measurements of the laser pulse energy, dura-
tion, and focal spot size. The largest magnetic fields
available terrestrially (~102 MG) are generated by explo-
sive ionization of a solid target with an intense ultra-
short laser pulse [7b]. In paper [7c] presented first ex-
perimental measurements of the temporal evolution of
megagauss magnetic fields generated at the critical lay-
er, on femtosecond time scales. The field generation and
decay mechanism are identified and the role of reso-
nance absorption (RA) was examined by authors of pa-
per [7c]. The field evolution was explained to be due to
currents generated by fast electrons [8a] and plasma re-
turn currents damped by turbulence induced resistivity
[8b]. Authors of paper [7c] first demonstrated ultrashort,
megagauss magnetic pulses , with a peak magnitude of
27 MG and 6 ps (FWHM) duration generated by a p-po-
larized laser pulse (1016 W/cm2, 100 fs). They observed
no significant Faraday rotation but large and easily mea-
surable ellipticity change. Authors emphasized that in
agreement with their observation a magnetic field gen-
eration primarily occurs near the critical surface (ne
~1021 cm-3), the region of maximum laser absorption.
Moreover, it is the magnetic field in the overdense re-
gion that determines hot electron transport into the bulk.
This indicates that a magnetic field (B) is essentially
perpendicular to the laser pulse propagation direction in
agreement with previous reports for RA generated mag-
netic fields [7b]. Such observations are the first evi-
dence of the large magnetic fields whose have been pre-
dicted to occur during laser - target interactions in dense
plasma [10].
5. RESULTS OF NUMERICAL SIMULATION
In [29] the problem of high-intensity, linearly polar-
ized electromagnetic pulse incident onto a collisionless
plasma layer is solved numerically in a Cartesian coor-
dinate system in a 2.5-D formulation (z is the cyclic co-
ordinate and there are three components of the momen-
tum) by means COMPASS (COMputer Plasma And
Surface Simulation) code. The recent review [30] and
references therein combine a detailed information con-
cerning COMPASS code as well as its possibilities and
applications. One of general advantage of the complete
numerical simulation is possibility as well as at the lab-
oratory experiments obtain all necessary information
concerning spatial and temporal dynamics of both parti-
cles and self-consistent electromagnetic fields without
usage of additional data (reflection and absorption coef-
ficients, changes of either a plasma temperature or dif-
ferent plasma parameters) in given situation at a interac-
tion intensive electromagnetic pulse with plasmas. We
give only the external parameters, the both initial and
bounded conditions for particles and fields and as re-
sults of a numerical simulation we attain all characteric-
tics of plasmas together with pulsed self-consistent elec-
tromagnetic fields. In given problem we consider at the
initial time, a cold motionless neutral two-component
(ions and electrons with a real ratio of their masses)
plasma with uniform density fills the whole right-hand
part of rectangular domain X×Y=Lx×Ly=128×64 pec ω/
(c is the speed of light, peω is the electron plasma fre-
quency). The line x = Lb=40 pec ω/ represents the plas-
ma-vacuum boundary. The system is periodical along
the y-coordinate; the plasma particles are reflected elas-
tically from the right-hand and left-hand boundaries.
The initial and boundary conditions for the electromag-
netic fields (they are measured in units ecme /0ω ) are
the following: E(t<0)=B(t<0)=0; Ey(x=0, y,
t>0)=Bz(x=0, y, t>0)=A(y)cos ( 0ω t); A(y)=A0exp ((y-
Ly)/l0)2, where 2/0 peωω = is the frequency of the in-
cident electromagnetic radiation. The radiation intensity
A0 provides a kinetic momentum of about 3mec to be
carried by oscillations; l0 =10 pec ω/ .
The most characteristic feature of the action of an in-
tense, normally incident electromagnetic pulse onto an
ultrahigh-density plasma consists in a “well-digging” ef-
fect. The depth of the “well” in the plasma profile in-
creases with time and is 15 pec ω/ at time 500 1−
peω .
Worth nothing is the growing in time sharp nonunifor-
mity of the perturbed plasma layer in the transverse di-
rection.
Thereby it shown that the magnetic field oscillates
with the doubled frequency of a laser radiation, but it
has unchanged direction. The magnetic field oscillations
are saw good at Fig.2. Now let us look at Figs.2,a and
2,b, which present two instantaneous magnetic field Bz
distributions separated in the time by 1−
peπ ω (a plasma
wave half-period). It will be noted that a maximum of
magnetic field (1.1) in the point (38,31) in the time
petω =200 (see Fig.2,a) after a plasma wave half-period
(see Fig.2,b) replaced in this point very low value of
magnetic field.
Fig.2 (from [29]) Spatial distribution of magnetic field
Bz at different times: petω =200(a); petω =200+π (b)
The magnetic field Bz attains its peak value of (0.64)
at the point (36.5,29), cf. Fig.2,b. It is shown that the
magnetic field Bz is consistent with a linearly modulated
current flowing along the line y=Ly/2. We do not ob-
serve this field to change its direction, but 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 maximum magnetic field. One
should note that the numerical simulation has been
made under very optimal conditions: a uniform plasma
density makes it sure a own plasma oscillation reso-
nance with a longitudinal modulation density of parti-
cles in a wave as well as a maximum frequency of non-
linear Tomson scattering spectrum. In experiments a
plasma inhomogeneity was very essential, with the re-
sult that resonant conditions were fulfilled only in a
small plasma region. Afterwards the interaction pulse,
only the “dc” magnetic field exists, as measured in the
underdense plasma region in [6].
On the basis of the formula
12/1222 ))(())/(10(2.4)( −−= mmWIxMGBdc µλ , where
I is the intensity of the incident laser radiation) one ob-
tains a “dc” magnetic field magnitude of few MG for
the experimental parameters of [6], and a few tens MG
for the experimental conditions of [7]. 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 [31].
By means of a 2.5 - dimensional numerical simula-
tion on the macroparticles method it is possible to find
the magnetic field spatial and temporal distribution
without usage an adapted parameter unlike of the con-
ventional Tnx∇∇ mechanism (see for example
[6,32]). On the other hand, theoretical model for the
generation of a magnetic field proposed by Sudan [10b]
is not appropriate, this model being very large ratio of
plasma density to critical density and when the
Tnx∇∇ contribution is not relevant.
The work by V.I. Karas` was supported in part by
the Cariplo Foundation (Como, Italy) and INTAS
project #01-233.
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Charged Particle Acceleration by an Intense Ultra-
short Electromagnetic Pulse Excited in a Plasma by
Laser Radiation or by Relativistic Electron Bunches
// Plasma Physics Reports. 2002, vol.28, p.125-140.
31. D.F. Price, R.M. More, R.S. Walling, G. Guethlein,
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Phys. Rev. Lett. 1995, vol.75, p.252-255.
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The interaction between intense laser radiation and matter is known to produce a wealth of nonlinear effects. Those include fast electron and ion generation [1–5] indicating that ultra-strong electric fields are produced in the course of the laser–plasma interaction. An equally ubiquitous, although less studied, effect accompanying laser–matter interaction is the generation of ultra-strong magnetic fields in the plasma [6–11]. Magnetic fields can have a significant effect on the overall nonlinear plasma dynamics. Extremely high (few megagauss) azimuthal magnetic fields play an essential role in the particle transport, propagation of laser pulses, laser beam self-focusing, penetration of laser radiation into the overdense plasma and the plasma electron and ion acceleration.
The generation of an axial magnetic field in the plasma by a circularly (or elliptically) polarized laser is often referred to as the inverse Faraday effect (IFE). First theoretically described by Pitaevskii [12] and Steiger and Woods [13] it results from the features of the electron motion in a circularly polarized electromagnetic wave. During the interaction of the plasma electrons with the circularly polarized laser pulse, electrons absorb both the laser energy and the angular momentum of the laser pulse. In particular, the angular momentum absorption leads to the electron rotation and generation of the axial magnetic field by the azimuthal electron current. Naturally, IFE does not occur for a linearly polarized laser pulse since it does not possess any angular momentum. IFE has since been measured in several experiments [9,14, 15]. The conditions under which IFE is possible are still not fully explored. What is theoretically known [16] is that there is no magnetic-field generation during the interaction of the inhomogeneous circularly polarized electromagnetic waves with the homogeneous plasma. Magnetic field can be produced in the presence the strong plasma inhomogeneity [17–19] either preformed or developed self-consistently during the interaction. More recently a mechanism has been proposed for the generation of an axial magnetic field through the transfer of the spin of the photons during the absorption of a transversely nonuniform circularly polarized radiation [20]. The magnetic field thus generated has a magnitude proportional to the transverse gradient of the absorbed intensity and inverse proportional to the electron density, the latter sealing being in contrast to earlier theories of IFE [20]. Along the same lines as [20], it has been demonstrated that in laser-plasma interactions strong axial magnetic fields can be generated through angular (spin) momentum absorption by either electron-ion collisions or ionization. Yet another mechanism of magnetic field generation has been proposed (in framework of classical electrodynamics) [21], based on the resonant absorption by energetic electrons of a circularly polarized laser pulse. The resonance occurs between the fast electrons, executing transverse (betatron) oscillations in a fully or partially evacuated plasma channel, and the electric field of the laser pulse. The betatron oscillations are caused by the action of the electrostatic force of the channel ions and self-generated magnetic field. This type of resonant interaction was recently suggested as a mechanism for accelerating electrons to highly relativistic energies [21,22]. When a circularly polarized laser pulse is employed, its angular momentum can be transferred to fast resonant electrons along with its energy. The resulting electron beam spirals around the direction of the laser propagation, generating the axial magnetic field [21]. In [21] the intensity of the magnetic field generated in relativistic laser channel was calculated taking into ac-count self-generated static fields, which are neglected in known IFE theories [17–19]. Calculations [21] are in agreement with the recent experiments at the Rutherford Appleton Laboratory (RAL) [15] which exhibited very large (several megagauss) axial magnetic fields during the propagation of a sub-picosecond laser pulse in a tenuous plasma. The relevant aspect of the RAL experiment is that both fast electrons and the strong magnetic field were measured in the same experiment.
In an underdense longitudinal inhomogeneous plasma the nonrelativistic two-dimensional treatment of self-generated magnetic fields was presented in the article [23], showing that a laser beam propagating along a density plasma gradient produces a rotational current which gives rise to a quasi-static magnetic field. An analogous mechanism was considered earlier in the paper [24] whereas the nonlinear mixing of two electromagnetic waves in a nonuniform plasma was discussed in the work [25]. They investigated a circularly polarized pulse for which the generation of low-frequency electromagnetic field is due to the inverse Faraday effect. In the extremely strong relativistic regime the magnetic field generated by the laser beams in underdense plasma was recently studied numerically [26]. The main objective of the work [18] was to investigate self-generated quasi-static magnetic fields both in the laser pulse body and behind the pulse in the region of the wake-field. Authors treated the laser radiation as linearly polarized and the plasma as uniform and underdense. The analytical work was based on a perturbation theory applied to the set of relativistic cold electron fluid equations and Maxwell’s equations. The quasi-static magnetic field generated by a short laser pulse in a uniform rarefied plasma is found analytically and compared to two-dimensional particle-in-cell simulations .It is shown that a self-generation of quasi-static magnetic fields takes place in fourth order with respect to the parameter vE/c where vE and c are the electron quiver velocity and the light speed, respectively. In the wake region the magnetic field possesses a component which is homogeneous in the longitudinal direction and is due to the steady current produced by the plasma wakefield and a component which is oscillating at the wave number 2kp,, where kp is the wave number of the plasma wake, a known property of nonlinear plasma waves [27,28]. Numerical particle simulations confirm the analytical results and are also used to treat the case of high intense laser pulses with vE/c >1. The resultant magnetic field has a focusing effect on relativistic electrons in the plasma wakefield accelerator context.
Further 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. [10] of the interaction of an ultraintense laser pulse with an overdense plasma target have revealed non-oscillatory self-generated magnetic fields up to 250 MG in the overdense plasma, that this nonoscillatory magnetic field 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 Fig.1, [6]. A high density plasma jet has been observed simultaneously with the magnetic fields by interferometry and optical emission.
In [29] the problem of high-intensity, linearly polarized electromagnetic pulse incident onto a collisionless plasma layer is solved numerically 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 COMPASS (COMputer Plasma And Surface Simulation) code. The recent review [30] and references therein combine a detailed information concerning COMPASS code as well as its possibilities and applications. One of general advantage of the complete numerical simulation is possibility as well as at the laboratory experiments obtain all necessary information concerning spatial and temporal dynamics of both particles and self-consistent electromagnetic fields without usage of additional data (reflection and absorption coefficients, changes of either a plasma temperature or different plasma parameters) in given situation at a interaction intensive electromagnetic pulse with plasmas. We give only the external parameters, the both initial and bounded conditions for particles and fields and as results of a numerical simulation we attain all characterictics of plasmas together with pulsed self-consistent electromagnetic fields. In given problem we consider at the initial time, a cold motionless neutral two-component (ions and electrons with a real ratio of their masses) plasma with uniform density fills the whole right-hand part of rectangular domain XY=LxLy=12864 (c is the speed of light, is the electron plasma frequency). The line x = Lb=40 represents the plasma-vacuum boundary. The system is periodical along the y-coordinate; the plasma particles are reflected elastically from the right-hand and left-hand boundaries. The initial and boundary conditions for the electromagnetic fields (they are measured in units ) are the following: E(t<0)=B(t<0)=0; Ey(x=0, y, t>0)=Bz(x=0, y, t>0)=A(y)cos (t); A(y)=A0exp ((y-Ly)/l0)2, where is the frequency of the incident electromagnetic radiation. The radiation intensity A0 provides a kinetic momentum of about 3mec to be carried by oscillations; l0 =10.
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. The depth of the “well” in the plasma profile increases with time and is 15 at time 500. Worth nothing is the growing in time sharp nonuniformity of the perturbed plasma layer in the transverse direction.
Thereby it shown that the magnetic field oscillates with the doubled frequency of a laser radiation, but it has unchanged direction. The magnetic field oscillations are saw good at Fig.2. Now let us look at Figs.2,a and 2,b, which present two instantaneous magnetic field Bz distributions separated in the time by (a plasma wave half-period). It will be noted that a maximum of magnetic field (1.1) in the point (38,31) in the time =200 (see Fig.2,a) after a plasma wave half-period (see Fig.2,b) replaced in this point very low value of magnetic field.
Fig.2 (from [29]) Spatial distribution of magnetic field Bz at different times: =200(a); =200+(b)
The magnetic field Bz attains its peak value of (0.64) at the point (36.5,29), cf. Fig.2,b. It is shown that the magnetic field Bz is consistent with a linearly modulated current flowing along the line y=Ly/2. We do not observe this field to change its direction, but 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 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 a plasma inhomogeneity was very essential, with the result that resonant conditions were fulfilled only in a small plasma region. Afterwards the interaction pulse, only the “dc” magnetic field exists, as measured in the underdense plasma region in [6].
On the basis of the formula
, 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 [6], and a few tens MG for the experimental conditions of [7]. 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 [31].
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 usage an adapted parameter unlike of the conventional mechanism (see for example [6,32]). On the other hand, theoretical model for the generation of a magnetic field proposed by Sudan [10b] is not appropriate, this model being very large ratio of plasma density to critical density and when the contribution is not relevant.
The work by V.I. Karas` was supported in part by the Cariplo Foundation (Como, Italy) and INTAS project #01-233.
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32.M. G. Haines. // Phys. Rev. Lett. 1997, vol.78, p.254–257.
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