Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil
The distribution of electrical potential and electron density near foil, resulting in vortical electron dynamics at interaction of an intensive laser pulse with a foil, is considered.
Збережено в:
| Дата: | 2009 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2009
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/88308 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil / V.I. Maslov, A.M. Yegorov, I.N. Onishchenko, O.V. Suhostavez // Вопросы атомной науки и техники. — 2009. — № 1. — С. 101-103. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-88308 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-883082015-11-12T03:02:29Z Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil Maslov, V.I. Yegorov, A.M. Onishchenko, I.N. Suhostavez, O.V. Плазменная электроника The distribution of electrical potential and electron density near foil, resulting in vortical electron dynamics at interaction of an intensive laser pulse with a foil, is considered. Показано, що при взаємодії інтенсивного лазерного імпульсу з фольгою розподіл електричного потенціалу і густин частинок є таким, що в околиці фольги динаміка електронів може бути вихровою. Показано, что при взаимодействии интенсивного лазерного импульса с фольгой распределение электрического потенциала и плотностей частиц таково, что в окрестности фольги динамика электронов может быть вихревой. 2009 Article Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil / V.I. Maslov, A.M. Yegorov, I.N. Onishchenko, O.V. Suhostavez // Вопросы атомной науки и техники. — 2009. — № 1. — С. 101-103. — Бібліогр.: 15 назв. — англ. 1562-6016 PACS: 52.27.Lw http://dspace.nbuv.gov.ua/handle/123456789/88308 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Плазменная электроника Плазменная электроника |
| spellingShingle |
Плазменная электроника Плазменная электроника Maslov, V.I. Yegorov, A.M. Onishchenko, I.N. Suhostavez, O.V. Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil Вопросы атомной науки и техники |
| description |
The distribution of electrical potential and electron density near foil, resulting in vortical electron dynamics at
interaction of an intensive laser pulse with a foil, is considered. |
| format |
Article |
| author |
Maslov, V.I. Yegorov, A.M. Onishchenko, I.N. Suhostavez, O.V. |
| author_facet |
Maslov, V.I. Yegorov, A.M. Onishchenko, I.N. Suhostavez, O.V. |
| author_sort |
Maslov, V.I. |
| title |
Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil |
| title_short |
Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil |
| title_full |
Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil |
| title_fullStr |
Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil |
| title_full_unstemmed |
Vortical electron dynamics in plasma, observed at interaction of laser pulse with foil |
| title_sort |
vortical electron dynamics in plasma, observed at interaction of laser pulse with foil |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2009 |
| topic_facet |
Плазменная электроника |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/88308 |
| citation_txt |
Vortical electron dynamics in plasma,
observed at interaction of laser pulse with foil
/ V.I. Maslov, A.M. Yegorov, I.N. Onishchenko, O.V. Suhostavez // Вопросы атомной науки и техники. — 2009. — № 1. — С. 101-103. — Бібліогр.: 15 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT maslovvi vorticalelectrondynamicsinplasmaobservedatinteractionoflaserpulsewithfoil AT yegorovam vorticalelectrondynamicsinplasmaobservedatinteractionoflaserpulsewithfoil AT onishchenkoin vorticalelectrondynamicsinplasmaobservedatinteractionoflaserpulsewithfoil AT suhostavezov vorticalelectrondynamicsinplasmaobservedatinteractionoflaserpulsewithfoil |
| first_indexed |
2025-07-06T16:04:08Z |
| last_indexed |
2025-07-06T16:04:08Z |
| _version_ |
1836914152856092672 |
| fulltext |
PLASMA ELECTRONICS
VORTICAL ELECTRON DYNAMICS IN PLASMA,
OBSERVED AT INTERACTION OF LASER PULSE WITH FOIL
V.I. Maslov, A.M. Yegorov, I.N. Onishchenko, O.V. Suhostavez2
NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2V.N. Karazin Kharkov National University, Kharkov, Ukraine
The distribution of electrical potential and electron density near foil, resulting in vortical electron dynamics at
interaction of an intensive laser pulse with a foil, is considered.
PACS: 52.27.Lw
1. INTRODUCTION
The interaction of an intensive laser pulse with a foil
with the purpose of ion acceleration investigates in the world
[1-9]. Laser acceleration of ions was observed from 1960s
[10]. The electron semi-vortex or vortex is formed near an
irradiated foil at certain conditions. We consider conditions
of semi-vortex formation at foil irradiation by laser pulse.
At effect of an intensive laser pulse on a metal foil
the high-energy electrons direct through it and form near
to a surface of the foil electron layer [1]. Thus electrons of
the foil receive a moment from the driver. During the
moment exchange the electrons get longitudinal Vqz and
radial Vqr velocities. At electron leaving from the isolated
foil the positive charge with surface density σ collects on
it. So besides the electrical potential of the volume charge
with amplitude -φd, which is formed by an electron layer
at the foil’s surface [1], the polarized electrical potential
φ0 is formed between the foil and this electron layer. σ is
arisen up to some value, when φo+φd reaches the electron
energy
φo+φd≈(mec2/e)(γq-1). (1)
At not large φd/φo<1 one can write approximately
σ≈mec2(γq-1)/4πe2∆ξq, (2)
After that the electrons come back to the foil. They come
back on larger radius, than they left foil. It is determined
by initial radial electron velocity Vqr, and also by their
scattering on r by an own volume charge. According to
[11] it can be also determined by magnetic pressure. If
radius of an electron flow, leaving the foil, rq is less in
comparison with the longitudinal dimension of area of
their braking rq<∆ξq, a coming back flow extends on r on
∆rw≈∆ξq. At certain conditions ∆ξq is the Debye radius of
high-energy (HE) electrons ∆ξq≈rdq [1]. Then we derive in
nonrelativistic approximation
σ≈(Vq/4e)(menq/π)1/2. (3)
This layer is extended L0(t) during ion acceleration up to
60 MeV [1].
If rq>>∆rw, the vortex is not formed. The vortex can
be formed, if rq<∆rw. At achievement of the flow velocity
Vz≈c one can derive for certain conditions
∆ξq≈c(γq-1)1/2/ωpq, σ≈(c/2e)(γq-1)1/2(menq/π)1/2 (4)
σ can be estimated from the balance of electron flows
σ≈2nqrq
2∆ξq/π(∆rw)2 (5)
One can see that σ is depended on ratio rq/∆rw.
2. ELECTRIC POTENTIAL DISTRIBUTION
AT ELECTRON FLOW LEAVING FROM FOIL
1D numerical simulation [12] has shown, that at
injection of a cold electron beam into plasma 0<z<L the
strongly nonlinear structure - jump of potential can be
formed near the plasma boundary. We consider properties
of similar connected jump and dip of electrical potential.
These jump and dip are formed by electrons, which are
accelerated by a driver at its interaction with a foil. We
will show, that at leaving of HE electron flow with
density nq from isolated foil into vacuum the jump and dip
of electrical potential, similar to [13], is possible to form
near the foil. These jump and dip return electrons to the
foil and accelerate ions. Let's consider at first the potential
distribution along axis of HE electron flow in one-
dimensional approximation in the case of relativistic HE
electrons.
The longitudinal structure of electrical potential
along axis of the narrow flow represents potential jump
near the foil and potential dip in the flow. In the limiting
case rq<<∆ξq the longitudinal electrical field along axis of
the flow can be presented approximately in the following
kind
Ez≈2πe{σ+nq[-2z+∆ξq+(rq
2+z2)1/2-(rq
2+(∆ξq-z)2)1/2 ]} (6)
The potential equals maximal value φo=φ(z=0) on the foil
and it equals zero in some point z0 inside the flow. On the
interval z0<z<∆ξq the electrical potential dip with
amplitude -ϕd is distributed.
We assume that electrons of a plasma layer formed
near the foil’s surface are low-energy. Then they quickly
fall on the foil. Thus near the foil single group of
electrons remains: HE electrons with density nq. The
longitudinal velocity of the polarized electrical potential
and of the volume charge potential is approximately equal
to velocity of front of accelerated ions. If HE electrons are
possible to present as a beam with finite energy width, far
from a point of their reflection their density grows from
the foil’s surface under the power law
nq(z)=nq(1-γq
-2)1/2[1-(1+eφ/mc2)-2]-1/2. (7)
The maximal negative charge nq
(max)=nq(2Vq/Vthq)1/2/γq
3/2 is
reached on some distance from the foil. Vthq is the thermal
velocity of HE electrons. If the distribution function of
HE electrons can be presented as equilibrium Maxwell
distribution function with temperature Tq, their density
falls down from the foil’s surface according the
exponential law
nq(z)=nqexp[(φ-φo)e/Tq] . (8)
With the help (7) one can show that at φc=(φo+φd)(2Vqth/c)γo
2
the reflection of HE electrons begins.
For essential ion acceleration, the considered quasi-
stationary distribution of the electrical potential should be
supported during long time. Electrons transfer a
momentum to the polarized electrical potential and to the
volume charge potential. The flow of momentum
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2009. № 1. 101
Series: Plasma Physics (15), p. 101-103.
transferred to the polarized electrical potential and to the
volume charge potential by reflected HE electrons equals
2nqmc2(γq
2-1)/γq (or nqTq). In a field of polarized electrical
potential and of volume charge potential ions receive a
momentum. The speed of increase of an ion momentum is
approximately equal to min0iLdVL/dt. L is the width of area
of ion acceleration. The ions also select energy from the
polarized electrical potential and from the volume charge
potential. The speed of energy selection by ions is
approximately equal to min0iLVLdVL/dt. The HE electrons
at interaction with the polarized electrical potential and
with the volume charge potential lose energy. The flow of
energy, transferred to the polarized electrical potential and
to the volume charge potential by HE electrons equals
nqmc22VL(γq
2-1)/γq (or VLnqTq). One can see that the
balance of energy flows is reduced to balance of
momentum flows. Using the balance of momentum flows
of particles, which interact with the polarized electrical
potential and with the volume charge potential, one can
derive approximately the expression for speed of ion
acceleration:
dVL/dt≈2nqmc2(γq
2-1)/γqmin0iL. (9)
That the HE electrons effectively accelerate ions and
not fall on walls, the radial forces should confine their in
the region of ion localization. As the low-energy electrons
quickly fall on the foil, one can write
n0i(z)≥nqγq
-2. (10)
from the condition of radial confinement of the HE
electrons. (10) is correct at semi-vortex or vortex
formation. The inequality (10) is correct at γq>>1, n0i<<nq
and at γq>1, n0i<nq.
Let's derive the equation, which describes a structure
of the polarized electrical potential and the volume charge
potential, and estimate their width. As the law-energy
electrons fall quickly on the foil, the structure of the
polarized electrical potential and of the volume charge
potential is determined by the HE electrons and by ions.
Integrating the Poisson’s equation on φ, neglecting the
small interval, closed φ=-φd, where the HE electrons are
reflected, in one-dimensional approximation we derive
(∂φ/∂z)2=(∂φ0/∂z)2-4πeσ(∂φ0/∂z)+8πmc2γqnq(1-γq
-2)1/2×
×{[[1-e(ϕ0-ϕ)/γqmc2]2-γq
-2]1/2-(1-γq
-2)1/2}-4πe∫n0i(z)dφ.(11)
Using the approached equality (ϕ0+ϕd) ≈ mc2(γq-1)/e and
condition ∂φ/∂z=0 at φ=-φd, we derive
∂φ0/∂z=2πeσ+
+{(2πeσ)2+4πγqmc2(1-γq
-1)[2nq(1+γq
-1)-n0i]}1/2. (12)
Let's obtain approximately width of the jump and dip:
Δz=(ϕ0+ϕd)/∂φ0/∂z≈ (13)
≈(c/ωpq0)√γq/[g+(g2+2-n0i/nq)1/2], g≡2πe2σ/ωpq0mc√γq
In the case of dense plasma its polarization δn=nq-n0i is
small. If selfconsistent ion dynamics follows for electric
field distribution such that δn≈const, one can obtain
Δz≈(c/ωpq0)√γq/[g+(g2+δn/nq)1/2].
Using (4), (5) one can obtain g≈rq
2/(∆r)2. One can see that
the electrical field is strengthened near foil by σ.
In approximation of the HE electrons as a thin flow
we obtain from (4)
ϕ(z)=ϕ0-2πeσz-πenq{rq
2×
×ln{[z+(rq
2+z2)1/2][∆ξq-z+(rq
2+(∆ξq-
z)2)1/2]/rq[∆ξq+(rq
2+∆ξq
2)1/2]}+ (14)
+∆ξq
2/2-(∆ξq-2z)2/2+z(rb
2+z2)1/2+
+(∆ξq-z)(rb
2+(∆ξq-z)2)1/2-∆ξq(rb
2+∆ξq
2)1/2,
0<z<∆ξq. The minimal value of the potential ϕmin equals
approximately at z≈∆ξq/2
ϕmin≈ϕ0-πeσ∆ξq-πenqrq
2ln(∆ξq/2rq) (15)
We derive approximately from (4)
∂φ0/∂z≈2πe(σ+nqrq) (16)
One can see that with decrease rq at nq=const ∂φ0/∂z
decreases. However, at focusing of the HE electrons with
their flow constancy the field, accelerating ions,
increases. Also one can see that the field, slowing down
of the thin flow of the HE electrons, is smaller in ωpqrq/c√
γq. Hence, the depth of penetration in plasma of the thin
flow of electrons is more and longitudinal size of the
semi-vortex or vortex in this case is more.
Because ϕ0≈2πσe(c/ωpq0)√γq, then
ϕmin/ϕ0≈-[πenqrq
2ln(∆ξq/2rq)]/[2πσe(c/ωpq0)√γq].
Let's consider the stability of relative electron flows
concerning HF perturbations on the basis:
1-α/z2-(1-α)[(z-y)-2+R(z+y)-2]/2γq
3=0 . (17)
α=n0e/n0i, z=ω/ωp , y=kVb/ωp , R is the parameter of radial
distance between direct and opposite electron flows. If
R=1, the counter electron flows are on the same radius.
From (17) it follows that in the region of jump and dip the
noise with the large phase velocities can be generated.
Similar to [12, 14] the noise does not destroy the jump
and dip due to: width of electron distribution function;
inhomogeneity of potential, which breaks the condition of
wave - particle resonance; and due to large relative
velocity of noise and jump. Also the noise does not
destroy the jump and dip due to decrease of n0e.
Let's consider the stability of relative electron flows
concerning LF perturbations on the basis:
1+α/(kd0)2-(1-α)[(z-y)-2+R(z+y)-2]/2γq
3=0 . (18)
d0=(T0e/4πn0e
2)1/2. From (18) one can show, that at R=1
and n0e, below critical, determined by the inequality
(Vtho/Vq)2/γq
3>α+(kd0)2 (19)
the potential jump becomes unstable relative
perturbations with small phase velocities. Thus, the
realization of counter electron flows as a vortex can
stabilize jump.
If the energy of the HE electrons concerns
nonrelativistic case, let us also consider this case. From
the kinetic eq. one can derive the electron distribution
function in 1D approximation, integrating which on
velocity, we obtain the density perturbation:
δn(φ)=ne-ni≈-ni+β, (20)
( )
[ ]
[ ]
[ ]
×
+π=β ∫∫
∞
−ϕ
−ϕ
−ϕ−ϕ
dV2n
qqo
qqo
qqo TV
TV
TV
q
( ) ( ) ( )2
2/12
qqo VexpTVV1 −
+ϕ−ϕ−×
−
From (20) one can see that the density of the HE electrons
increases. This results in negative volume charge. The
maximal value nq is reached in the region of strong
electron braking:
nq(φc)≈nqVq/(Vq(Tq/2)1/2)1/2=nq(Vq(2/Tq)1/2)1/2 . (21)
At φ1=φo-(Vq-(2Tq)1/2)2 the reflection of the HE electrons
begins.
102
From balance of momentum flows we derive
similarly to (9):
dVL/dt≈2nqmVq
2/min0iL (22)
We determine width of jump and dip from (20)
similarly to (13):
Δz=(ϕ0+ϕd)/∂φ0/∂z. (23)
∂φ0/∂z=2πeσ+[(2πeσ)2+8πmVq
2(nq-n0i/4) ]1/2.
One can see that the charge accumulation on the foil
strengthens the accelerating field. If the distribution
function of HE electrons can be presented as equilibrium
Maxwell distribution function with temperature Tq, in
approximation eσ<<Vq(2mnq/π)1/2 we obtain from (23)
∂φ0/∂z∼(Tqnq)1/2. With increase nq and Tq the field grows
and reaches 10 GV/cm for nq≈1023cm-3 and Tq≈1 keV [1].
Thus, using (3), we obtain
Δz≈4Vq/ωpq. (24)
In the case of small polarization δn=nq-n0i<<n0i of dense
plasma, consisting from HE electrons and ions, one can
estimate
Δz≈4(Vq/ωpq)(nq/δn)1/2.
The electrons are extended in the first front of the flow
due to the initial radial velocity, obtained as a result of
scattering, and due to strong volume charge of the flow.
On the foil large σ is supported, which influences on the
electron flow dynamics. The electron dynamics can be
represented as semi-vortex or vortex.
The vortical electron trajectories are described by
∂z[Vz
2/2-(e/me)ϕ]=-Vr∂rVz, ∂r[Vr
2/2-(e/me)ϕ]=-Vz∂zVr.
Introducing radius of curvature of electron trajectories
in the semi-vortex or vortex, one can derive balance of
forces, effecting on electron. From this balance one can
conclude that the vortex’s radius is close to longitudinal
its dimension.
Also the vortical electron trajectories are described
by the equation
[ ]η=ε∇
,V , ε≡V2/2-ϕe/me (25)
One can see that the spatial change of value meV2/2-eϕ is
determined by vorticity [ ]V
×∇≡η . From this relation
we derive for η
[ ] 2V,V ε∇−=η
. (26)
The electron trajectories form the semi-vortex in the
region of essentially 3D distribution of an electrical field.
For the vortex description we also use eq. [15]
( )( ) ( )( )Vnnd He
1
eeHet
∇ω−η=ω−η − . (27)
As η=η θe
and all is homogeneous on azimuth, for
nonrelativistic electrons we obtain
( )( ) 0nV e =η∇
, ne=n+∆ϕ/4πe (28)
One can see that the maximal vorticity is reached in the
region of the largest electron density inside the region of
volume charge.
In such electrical field the ions of a plasma layer,
formed near foil, are accelerated [1]. The similar ion
acceleration by the virtual cathode, formed by electron
beam, was observed earlier. The ions are accelerated by
volume charge of the HE electrons [1], and by polarized
potential, appeared between the isolated foil and electron
layer.
The energy of accelerated ions can be determined by
potential of shock and dip ε(i)≈Tq. If the accelerated ions
interact with shock and dip for a long time and ion
velocity is achieved to velocity of electron flow, which
determine structure and value of an accelerating field, the
maximal ion energy ε(i)
max equals
ε(i)
max≈Tqmi/me. (29)
In experiments (see [1]) ε(i)
max=60MeV was achieved.
REFERENCES
1. M. Borghesi. // 10th Easter Plasma Meeting. Cairo,
Egypt, 16-18 March 2008.
2. T.Okada et al. Phys. Rev. E. 2006. V. 74. P. 026401.
3. T.Ceccotti et al. PRL. 2007. V. 99. P. 185002.
4. T.V.Liseikina, A. Macchi. Appl. Phys. Let. 2007. V. 91.
P. 171502.
5. Y.T.Li et al. PRL. 2007. V. 99. P. 185002.
6. L.Romagnani et al. PRL. 2005. V. 95. P. 195001.
7. Min-Qing He et al. Phys. Rev. E. 2007. V. 76. P.
035402.
8. A. P. L Robinson et al. Phys. Rev. E. 2007. V. 75. P.
015401.
9. H.Chen et al. Phys. Rev. E. 2007. V. 76. P. 056402.
10. A.V. Gurevich et al, Sov. Phys. JETP. 1966. V. 22. P.
449.
11. S.V.Bulanov, T.Zh.Esirkepov. PRL. 2007. V. 98. P.
049503.
12. Singh N., Schunk R.W. Plasma Phys. and Contr. Fus.
1984. V. 26. P. 859.
13. Maslov V.I. Plas. Phys. Rep. 1992. V. 18. P. 1310.
14. Okuda H. et al. // Phys. Fluids. 1987. V. 30. P. 200.
15. V.I. Maslov, F. Porcelli. // Proc. of 17th Toki Conf. on
Phys. of Flows and Turb. Oct. 15, 2007. Toki. P. 179.
Article received 8.10.08
ВИХРЕВАЯ ДИНАМИКА ЭЛЕКТРОНОВ В ПЛАЗМЕ, НАБЛЮДАЮЩАЯСЯ ПРИ
ВЗАИМОДЕЙСТВИИ ЛАЗЕРНОГО ИМПУЛЬСА С ФОЛЬГОЙ
В.И. Маслов, А.М. Егоров, И.Н. Онищенко, О.В. Сухоставец
Показано, что при взаимодействии интенсивного лазерного импульса с фольгой распределение
электрического потенциала и плотностей частиц таково, что в окрестности фольги динамика электронов может
быть вихревой.
ВИХРОВА ДИНАМІКА ЕЛЕКТРОНІВ В ПЛАЗМІ, ЯКА СПОСТЕРІГАЄТЬСЯ ПРИ ВЗАЄМОДІЇ
ЛАЗЕРНОГО ІМПУЛЬСУ З ФОЛЬГОЮ
В.І. Маслов, О.М. Єгоров, І.М. Онишенко, О.В. Сухоставець
Показано, що при взаємодії інтенсивного лазерного імпульсу з фольгою розподіл електричного потенціалу і
густин частинок є таким, що в околиці фольги динаміка електронів може бути вихровою.
103
1. INTRODUCTION
REFERENCES
|