Radial acceleration and cumulation of ions by an intense converging ring laser pulse
Cumulation dynamics and acceleration of deuterium plasma ions by a focused ring laser pulse of the femtosecond duration are theoretically investigated. Laser pulse is focused by a dielectric lens. The spatial structure of ring laser pulse field in the vicinity of the lens focus is determined. The...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Radial acceleration and cumulation of ions by an intense converging ring laser pulse / V.A. Balakirev, I.N. Onishchenko, A.I. Povrozin, A.P. Tolstoluzhsky, A.M. Yegorov // Вопросы атомной науки и техники. — 2008. — № 4. — С. 77-82. — Бібліогр.: 4 назв. — англ. |
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irk-123456789-1103332017-01-04T03:03:07Z Radial acceleration and cumulation of ions by an intense converging ring laser pulse Balakirev, V.A. Onishchenko, I.N. Povrozin, A.I. Tolstoluzhsky, A.P. Yegorov, A.M. Новые методы ускорения заряженных частиц Cumulation dynamics and acceleration of deuterium plasma ions by a focused ring laser pulse of the femtosecond duration are theoretically investigated. Laser pulse is focused by a dielectric lens. The spatial structure of ring laser pulse field in the vicinity of the lens focus is determined. The values of cumulation coefficient of ions, their energy, and cumulation region dimensions are obtained. Conclusions are made about the possibility of the neutron source elaboration on considered cumulation principle. Досліджена динаміка кумуляції і прискорення іонів дейтерієвої плазми сфокусованим кільцевим лазерним імпульсом фемтосекундної тривалості. Визначена просторова структура поля кільцевого лазерного імпульсу поблизу фокуса лінзи. Отримані значення коефіцієнта кумуляції іонів, їх енергії та розміри області кумуляції. Зроблені висновки відносно можливості розробки нейтронного джерела на принципі кумуляції, що розглядається. Исследована динамика кумуляции и ускорения ионов дейтериевой плазмы сфокусированным кольцевым лазерным импульсом фемтосекундной длительности. Определена пространственная структура поля кольцевого лазерного импульса в окрестности фокуса линзы. Получены значения коэффициента кумуляции ионов, их энергии и размеры области кумуляции. Сделаны выводы относительно возможности разработки нейтронного источника, основанного на рассматриваемом принципе кумуляции. 2008 Article Radial acceleration and cumulation of ions by an intense converging ring laser pulse / V.A. Balakirev, I.N. Onishchenko, A.I. Povrozin, A.P. Tolstoluzhsky, A.M. Yegorov // Вопросы атомной науки и техники. — 2008. — № 4. — С. 77-82. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 41.75.Jv; 42.60.-v; 52.38.Kd http://dspace.nbuv.gov.ua/handle/123456789/110333 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц |
| spellingShingle |
Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц Balakirev, V.A. Onishchenko, I.N. Povrozin, A.I. Tolstoluzhsky, A.P. Yegorov, A.M. Radial acceleration and cumulation of ions by an intense converging ring laser pulse Вопросы атомной науки и техники |
| description |
Cumulation dynamics and acceleration of deuterium plasma ions by a focused ring laser pulse of the femtosecond
duration are theoretically investigated. Laser pulse is focused by a dielectric lens. The spatial structure of
ring laser pulse field in the vicinity of the lens focus is determined. The values of cumulation coefficient of ions,
their energy, and cumulation region dimensions are obtained. Conclusions are made about the possibility of the
neutron source elaboration on considered cumulation principle. |
| format |
Article |
| author |
Balakirev, V.A. Onishchenko, I.N. Povrozin, A.I. Tolstoluzhsky, A.P. Yegorov, A.M. |
| author_facet |
Balakirev, V.A. Onishchenko, I.N. Povrozin, A.I. Tolstoluzhsky, A.P. Yegorov, A.M. |
| author_sort |
Balakirev, V.A. |
| title |
Radial acceleration and cumulation of ions by an intense converging ring laser pulse |
| title_short |
Radial acceleration and cumulation of ions by an intense converging ring laser pulse |
| title_full |
Radial acceleration and cumulation of ions by an intense converging ring laser pulse |
| title_fullStr |
Radial acceleration and cumulation of ions by an intense converging ring laser pulse |
| title_full_unstemmed |
Radial acceleration and cumulation of ions by an intense converging ring laser pulse |
| title_sort |
radial acceleration and cumulation of ions by an intense converging ring laser pulse |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2008 |
| topic_facet |
Новые методы ускорения заряженных частиц |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/110333 |
| citation_txt |
Radial acceleration and cumulation of ions by an intense converging ring laser pulse / V.A. Balakirev, I.N. Onishchenko, A.I. Povrozin, A.P. Tolstoluzhsky, A.M. Yegorov // Вопросы атомной науки и техники. — 2008. — № 4. — С. 77-82. — Бібліогр.: 4 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T00:29:23Z |
| last_indexed |
2025-07-08T00:29:23Z |
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| fulltext |
RADIAL ACCELERATION AND CUMULATION OF IONS
BY AN INTENSE CONVERGING RING LASER PULSE
V.A. Balakirev, I.N. Onishchenko, A.I. Povrozin, A.P. Tolstoluzhsky, A.M. Yegorov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: onish@kipt.kharkov.ua
Cumulation dynamics and acceleration of deuterium plasma ions by a focused ring laser pulse of the femto-
second duration are theoretically investigated. Laser pulse is focused by a dielectric lens. The spatial structure of
ring laser pulse field in the vicinity of the lens focus is determined. The values of cumulation coefficient of ions,
their energy, and cumulation region dimensions are obtained. Conclusions are made about the possibility of the
neutron source elaboration on considered cumulation principle.
PACS: 41.75.Jv; 42.60.-v; 52.38.Kd;
INTRODUCTION
Development of a compact bright neutron sources is
an actual problem of modern nuclear physics. Such
sources can be used in crystal material spectroscopy, for
nuclear reactions initiation, isotope production and other
applications.
In [1] the method of neutron production based on the
effect of dense plasma ions cumulation under influence
of a focused ring laser pulse has been proposed and in
[2] it was applied for so called “light trap”. The essence
of this method is following. Under the action of pon-
deromotive force on plasma electrons a charge separa-
tion in radial direction occurs. Arisen electric field of
the space charge imposes to plasma ions (e.g., deuter-
ons) the radial momentum, directed to the axis of the
system. The high increase of the ion density in the axis
region and ions acceleration induces thermonuclear
flash along with intensive neutron flux.
In the present work the cumulation effect and accel-
eration of ions by the ring laser pulse focused by the
lens is theoretically investigated. The work consists of
two sections. In the first section a ring laser pulse focus-
ing process of the femtosecond range duration by the
double-convex lens is considered. It is shown that in the
vicinity of the focal plane, as a result of diffraction di-
vergence of the ring wave beam, the transformation of
the ring wave beam into the pulse with approximately
Gaussian transversal distribution of the intensity takes
place. Such complicated structure of the laser pulse
wave beam results in a number of peculiarities of radial
cumulation process and ions acceleration by the focused
laser pulse.
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2008. № 4.
Серия: Плазменная электроника и новые методы ускорения (6), с.77-82. 77
The second section is devoted to the study of the ion
cumulation dynamics created by the focused ring laser
pulse. The degree of ion cumulation in the axes region
and ion energy is determined. In comparison with our
previous paper [3] the effect of ions acceleration out of
focal region is investigated too.
1. FIELD OF RING LASER PULSE
FOCUSING BY DIELECTRIC LENS
A laser pulse is incident on thin bifocal lens with the
material permittivity ε . We will describe the pulse
electromagnetic field by scalar function
which can be one of electromagnetic field component.
Directly before lens the function u is represented as
( , , , )u x y z t
0 0 0 0 0( , , 0, ) ( ) ( , )u x y z t u t x y= = Ψ Φ , (1.1)
where 0( ) ( / ) cosLt F t t tωΨ = describes dependence in
time of the pulse laser field, function ( / )LF t t is the
pulse laser envelope, 0ω is the carrier frequency, Lt is
the characteristic pulse duration, 0 0( , )x yΦ is the func-
tion describing transversal field distribution directly
immediately before lens.
According to the Fourier-transform formalism in-
stead of (1.1) we have
0 0 0 0 0( , ,0) ( ) ( , )u x y u x yω ω= Ψ Φ
)
,
where
, (1.2) 0( ) ( / ) cos( ) i t
LF t t t e dtωω ω
∞
−∞
Ψ = ∫
)
and
0 0 0 0 0
1( , ,0, ) ( , ) ( )
2
i tu x y t u x y e dtωω
π
∞
−
−∞
= Φ Ψ∫
)
(1.3)
A thin spherical lens as a phase corrector [3] is con-
sidered. Then the field after lens can be expressed as
0 0 0 0( , , ) ( , ,0)u x y d Tu x yω ω=
)
,
where
20
0 02
k
ik nd i r
fT e
−
=
)
, 2 2
0 0r x y= + 0 , is the
maximal lens thickness,
d
n ε= , 0 /k cω= c, is light
velocity, f is the focal lens distance.
The field over the space after the lens can be ex-
pressed through the Green function
0 0 0 0 0 0( , , ) ( , , ) ( , , )
S
u x y z dx dy u x y d G x x y y zω ω ω= −∫ − . (1.4)
Here
2 20
0 0[( ) ( ) ]0 2
0 0( , , )
2
k
ik z i x x y y
zk
G x x y y z e
izω π
+ − + −
− − = 0
is Green function of the parabolic equation [3]. Pass in
(1.4) into cylindrical system of coordinates. As result
instead of (1.4) we obtain
22 0 0
0 0( ) 20 02
0 0 0 0 0
0
( ) ( ) ( )
k rar iik z nd ik
zk k
u u e r dr r J e
iz z
0rr ζ
ω ω
+ +
= Ψ Φ∫
)
,(1.5)
where is the lens radius, a 1 1 1
z fζ
= − .
Accordingly for the field of laser pulse we have the
following expression
2
0 0
20 0
78
0rr
0 0 0 0
0
( , , ) ( ) ( ) ( )
2
k ra i
i Tu k
u r z t d e r dr r J e
icz z
ω
2
2
ln(1/ )22 4
41 1
max2 max2 02 2
0 1
2 ln(1/ )2 , , ( )
1
s
slf sr r r I r I s e
k r s f
−
− −
∗ ∗= = =
−
ω ω ω
π
∞
−
−∞
= Ψ Φ∫ ∫
)
, ζ
21 ( )
2
rT t z nd
c z
= − + −
c
. For the pulse with Gaussian
envelope 2 2( / ) exp( / )L LF t t t t= − we have
2 2 2 2
0 0
1 1( ) ( )
4 4( ) [ ]
2
L Lt t
Lt e e
ω ω ω ωπω
− − − +
Ψ = +
)
.
Let’s consider the following model transversal pro-
file of the ring laser pulse
2 2 2 2
0 1 0 2/ /
0( ) r r r rr e e− −Φ = − , . 1 2r rf
This function turns to zero at and reaches the
maximal values at the point
0r =
2
max 2 2
ln(1/ )
1
sr r
s
=
−
, 2 1/s r r= .
Edge effects caused by lens aperture finiteness, can
be neglected if . In this limit case in the integral
(1.5), the upper limit can be replaced with the infinity.
As a result we obtain the standard integral, which calcu-
lation gives the following expression for the laser pulse
field
1a r
0( , , ) ( ) ( , , )
4
i Tu
u r z t d B r z e
icz
ωω ω ω ω
π
∞
−
−∞
= Ψ∫
)
, (1.6)
where
2 2
1
2 2 2 2
1 21
2 2
21 12 2
1 / 1 /1 2
1 2
( , , )
1 / 1 /
l lr r
il ilz r z rr rB r z e e
il il
2ζ ζω
ζ ζ
− −
− −= −
− −
,
2
1,2 0 1,2 / 2l k r= .
Further we explore the expression for the laser pulse
field. First of all we shall note that at the focal plane
case the integral (1.6) can be calculated exactly.
Accordingly, for the laser pulse field we have the fol-
lowing expression
z f=
2 2 2 2
1
2 2 2 2
1 1 1
2 2 2 2
2
2 2 2 2
2 2 2
2
0 1
0 2
0 1 1
2
2
0 2
2 2
( , , ) cos( )
cos( ) .
L
L
l t r T
f rL L
l t r T
f rL L
u l t tdu z f r t e T
dt f
l t te T
f
τ τ
τ τ
ω
ω τ τ
ω
τ τ
− −
− −
⎡
⎢= =
⎢
⎣
⎤
−
⎥−
⎥
⎦
(1.7)
Here . 2 2 2 2 2
1,2 1,2 /Lt r r c fτ = + 2
For paraxial region expression for the
pulse field (1.7) is simplified. As a result for averaging
over carrier frequency intensity
1/Lt cf r r
2I u= we find
2
22
0 ( )L
T
tI I e F r
−
= ,
2 22 2
1 2
2 2 2 2
1
2
1 2( )
l lr r
f r f rl lF r e e
f f
− −⎛ ⎞
⎜ ⎟= −
⎜ ⎟
⎝ ⎠
2 . (1.8)
The function ( )I r has two maxima at points
2
2 21
max1 0 20, (0) (1 ) ,
l
r I I s
f
= = −
and one minimum at the point
min min0, ( ) 0.r I r= =
The ratio of maximal intensity values is equal to
2
2
ln(1/ )4
4 1
max 2
(0) 1.
( )
s
sI s e
I r
−=
The value of intensity in the first maximum always
exceeds intensity of the second maximum. Thus, origi-
nally ring laser pulse in the focal plane is transformed
into a continuous pulse.
For the quasi-monochromatic laser pulse
0 1Ltω (1.9)
integral (1.6) can be calculated approximately and in
that way to find the pulse field distribution all over the
space. For this purpose we transform the integral (1.6)
to the form
0
4
u dSu
cz dtπ
= ,
2 21
4 ( , , , )
2
Li T t
LS t e Q r z t d
ω ωπ ω ω
∞
− −
−∞
= ∫ , (1.10)
0 0
0 0( , , , ) ( , , ) ( , , )i T i TQ r z t e B r z e B r zω ωω ω ω ω−= + + +ω .
The main contribution to the integral (1.10) gives the
vicinity of the point 0ω = . The approximate calcula-
tion of the integral in this limit case gives the following
expression
0 0
0 0( , , ) (0, , , ) ( , , ) ( , , ).i T i TS r z t Q r z t e B r z e B r zω ωπ ω ω− ∗= = +
In the limit case (1.9) for laser pulse intensity we
have the following expression
2 22 /
0( , , ) ( , ),LT tI r z t I e F r z−= (1.11)
2 2
2 21 2
1 22 2
1 2 1 2
1 2 1 2 1 2
( , ) (1 ) (1 )
2 (1 )cos( ) ( )sin( )
l l
F r z R R
l l l l
R R
ζ ζ
θ θ θ θ
ζ ζ ζ ζ
⎧
= + + + −⎨
⎩
⎫
,
⎡ ⎤⎪− + − + + − ⎬⎢ ⎥
⎪⎣ ⎦⎭
2
2 21 /
2 2
1
1 /
ll
R e
z l
α
α
ρ
ζα
α
α ζ
−
+=
+
,
l r
z r
α
α
α
ρ = ,
2
2 2
/
1 /
l
l
α
α α
α
ζ
θ ρ
ζ
=
+
, 1, 2α = .
At the focal plane z f= , from expression (1.11) the
expression (1.8) follows. Let’s analyze obtained expres-
sion for some limit cases. First of all we will give distri-
bution of laser pulse intensity along the axis of the sys-
tem 0r =
2 2
2 2
2 / 1 2
0 2 2 2 2 2 2 2 2
1 2
( )
( / )( /
LT t z l l
I I e
)z l z f z l z f
− −
=
+ Δ + Δ
, (1.12)
.z f zΔ = −
The intensity increases on the axis and reaches max-
imum value in the focus z f= .
Far from the focus
2
0 22 /z zf k rΔ (1.13)
spatial distribution of the intensity is described by the
expression
2 2
2 2 2 2
2 2 2 2
1 2
2 /
0
2
2
2
( , , ) ( , ),
( , ) ( ) .
LT t
r f r f
r z r z
I r z t I e F r z
fF r z e e
z
−
− −
Δ Δ
=
= −
Δ
(1.14)
In the space region given by (1.13) focusing of the pulse
occurs with the initial ring configuration. The ring pulse
radius decreases with approaching towards the focus
according to the low
2
2
max 2
ln(1/ ) .
1
r sr z
f s
= Δ
−
Note that the laser pulse energy flow in the process
of focusing is conserved
0 0
( , , ) ( , 0, )rdrI r z t rdrI r z t
∞ ∞
= =∫ ∫ .
79
Fig.1. Radial profiles of laser pulse
Fig.1 shows radial laser pulse profiles at different
distances from the focus, calculated using the formula
(1.11). Numerical calculations were performed for the
lens with the focal distance f =10 cm, laser pulse wave-
length 1.05 mλ μ= , and geometrical parameters
cm, cm. 1 3r = 2 2r =
In the plane of the lens ( the radius of ring la-
ser pulse is cm. According to the formula
(1.14), at large distances from the focus the pulse has a
ring transversal structure (Fig.1,z4,z5). With approach-
ing to the focus, diffraction diffusion of the ring pulse
increases and, it transforms gradually into a continuous
pulse. According to formula (1.8), in the focal plane
(Fig.1,z0) near the axis region the transversal
pulse profile has a similar to the Gaussian shape.
0)z =
max 2.4r =
z f=
Fig.2 shows longitudinal coordinate intensity de-
pendences for various radius values. Near the axis re-
gion (Fig.2,r0,r1), in the focus, the intensity increases
greatly. With moving away from the axis in a focal
plane, intensity minimum is formed (Fig.2,r2,r3). With
moving away from the axis in a focal plane, intensity
minimum is formed (Fig.2,r2,r3). The curve of the lon-
gitudinal coordinate intensity dependence is two-
humped one. For the large radius values (Fig.2,r4,r5) in
the focus region the intensity decreases practically to
zero.
Fig.2. Longitudinal distribution of the intensity
2. ION CUMULATION BY RING LASER
PULSE
Let’s consider cumulation of ions by the focused
ring laser pulse in the uniform homogeneous cylindrical
plasma column, located symmetrically to the right and
left side of the lens focus. Axes of the plasma column
and the lens coincide.
In the previous section it has been shown that the la-
ser pulse conserves its original ring profile in the focal
region at distances from the focus 2
2/( )z f rλ πΔ 2 . For
the given lens and laser pulse parameters this inequality
is equivalent to the inequality 6z mμΔ . In this area
the transversal laser pulse structure is more favorable
for the paraxial cumulation of ions. The intensity maxi-
mum is located on the axis, near the focus; therefore
defocusing force will influence on plasma electrons and
accordingly also on plasma ions, removing plasma from
the axis to the periphery.
Under the laser pulse influence, the ponderomotive
force will affect plasma electrons
2 ,p pF mc= − ∇Φ
r
where is the electron mass, m 21 /p aΦ = + 2 is the
ponderomotive potential, 2 2 2/( ) .a e I mcω= A numerical
value of the dimensionless value a can be written
down in the form 9 20.85 10 ( ) ( / )m I W сmλ μ−= ⋅a . Un-
der the influence of the ponderomotive forces in plasma
the displacement of electrons relatively to ions will oc-
cur. As a result, in plasma the polarization electric field
E
r
will arise. The equation of motion for plasma elec-
trons has the form
2 ,e
p
dp
eE mc
dt
= − − ∇Φ
r r
where epr is the electron momentum. In the electric
field of the space charge plasma ions will begin to move
too. We have the following equation of motion for ions
,idv
M eE
dt
=
r r
M is the ion mass, ivr is their velocity. Plasma electrons
will be in equilibrium state at the polarized electric field
value
2
.p
mcE
e
= − ∇Φ
r
Correspondingly, the equation of motion of ions in this
approximation has the form [1]
2 21 / 2idv m c a
dt M
= − ∇ +
r
80
. (2.1)
Thus, the laser pulse influences on plasma ions through
the space charge field, arising as a result of a charge
separation in plasma.
Taking into account the very short time of the laser
pulse action on ions, the displacement of ions can be
neglected. In this approximation the ions acquire finite
velocity, and then they move uniformly and rectilinearly
by inertia. Integrating the equations of motion over the
time of the laser pulse influence, we find velocity, ac-
quired by the ions during the pulse propagation [2]
2 2 0 0
0
0
( , )
,
2 2ir L
F r zmv c t a
M r
π ∂
= −
∂
2 2 0 0
0
0
( , )
,
2 2iz L
F r zmv c t a
M z
π ∂
= −
∂
(2.2)
where are the initial coordinate values. These rela-
tions for velocity components are obtained for a com-
paratively low laser intensity In the oppo-
site limit case instead of (2.2) we have
0 0,r z
2 / 2 1.a
2 / 2 1a
0 02
0
0
( , )
,
2ir L
F r zmv c t a
M r
π ∂
= −
∂
0 02
0
0
( , )
2iz L
F r zmv c t a
M z
π ∂
= −
∂
. (2.3)
Cumulation process and acceleration of deuterium
ions by the focused ring laser pulse were investigated
numerically by solution of motion equation for ions
(2.1).
The calculated plasma region is shown in Fig.3
( 0τ = ). Left boundary of the area is at the distance of
39 mμ from the focus, the region length is 13 mμ , and its
radius is 12.7 mμ . Deuterium plasma of density
∼1020cm-3 is simulated by 52.3 10iN = ⋅ ion macroparti-
cles. Ions were placed in the calculated region accord-
ingly to the random low. Each red and blue point in
Fig.3 ( 0τ = ) corresponds to the initial position of ions.
Laser pulse parameters are as follows: wavelength
1.05 ,mλ μ= pulse duration , 400Lt fs= 1 3r cm= ,
. Maximum power density of the laser radia-
tion at the entrance plasma boundary is
2 2r c= m
19 2
max 1.2 10 /I W cm= ⋅ , i.e. the laser pulse parameter is
. 4.7a ≈
Fig.3 shows ion planes at the different points of
dimensionless time
,r z
/ Lt tτ = . At first in plasma the thin
compacting shell of conical configuration is formed,
which moves to the system axis and at moment
5.806τ = it reaches the left plasma boundary, where
laser pulse is the most focused. The radial size of cumu-
lation region is equal to one micron. Further, the ions
reach the axis, and begin to move away in the radial
direction, and the cumulation region spreads into plasma.
Fig.3. Ion plane at different moment
of dimensionless time
,r z
In other words, the laser pulse divergence results in
a cumulation wave formation in plasma, which moves
along the longitudinal direction of the field decreasing.
With the wave propagation its velocity decreases. It is
caused, firstly, by decreasing of radial ion velocity dur-
ing removing apart from the left plasma boundary and,
secondly, by increasing of shell radius. It should be note
that the longitudinal movement of ions is very slow and
practically it does not influence on radial cumulation.
Fig.4. Distributing of cumulation ion factor in plane
r , z at different moments of time
Fig.4 shows the coordinates dependences
of the cumulation coefficient at various points of time.
The cumulation coefficient was determined as a ratio of
ion density at the current moment of time at given point
to the initial density. It is seen from the figures that in
complete accordance with previous Fig.3 the effective
cumulation region moves deep into plasma. At the same
time the peak value of cumulation coefficient increases
in the process of cumulation wave propagation deep into
plasma. It is caused by increase of the ring laser pulse
radius, and consequently the number of ions entrained
in the process of ionic shell cumulation is increased too.
( , )K r z
As for the ion energy in the cumulation region (see
Fig.5) it is decreases continuously with time. Thus, if at
the moment of time 5.032τ = maximal ion energy
value equals to about 230 keV at the cumulation coeffi-
cient value , then at the moment of time 340K =
8.129τ = ion energy decreases to 100 keV with cumu-
lation coefficient increase up to the value of 460K = .
Fig.5. Distributing of ion energy in plane r , z
at different moments of time
As it follows from the relations (2.2) and (2.3) radial
ion velocity and consequently energy too, is propor-
tional to the influencing force. Since after the lens the
ring pulse radius increases quickly then the radial force
and consequently accelerated ion energy decreases.
3. IONS ACCELERATION
IN THE FOCAL REGION
Let's examine now a case, when the region in the vicin-
ity of the dielectric lens focus, i.e. f L z f L+ ≤ ≤ −
(2L = 80μ is the length of the focal region), is also in-
cluded into consideration. The numerical analysis of
ions dynamics in the laser pulse field have been exam-
ined for p pf
81
L z f L+ ≤ ≤ − , where 2L = 120 μ is the
length of the plasma column. In Fig.6 the obtained con-
figurational space (ri, zi) is shown for the various mo-
ments of time.
Fig.6. Configurational plane (r, z) for ions for
various moments of time
In the focal region, ions are experienced strong de-
focusing radial and longitudinal forces. Action of these
forces leads to leaving of ions from the focal region
(Fig.6, τ = 4.913). As a result a cavity is formed in
plasma. Further the size of the cavity increases (Fig.6,
τ = 8.693). Ions, which initially were located in the vi-
cinity of the focal plane, are experienced strong accel-
eration in radial direction. So the energy of a main bulk
of ions reaches 6 МeV. A small group of ions gains en-
ergy up to 23 МeV. It should be noted, that, as it is
shown in the previous section, far enough from the focal
plane, where the laser pulse has ring radial structure,
cumulation of ions and their radial acceleration directed
to plasma column axis takes place.
CONCLUSIONS
The cumulation of deuterium ions and ion accelera-
tion process induced by the femtosecond focused laser
pulse was investigated. Focusing is accomplished by the
means of double-convex lens. By the solution of the
corresponding quasioptical problem the spatial distribu-
tion of intensity after the lens was obtained. It was
shown that when the ring laser pulse approaches to the
lens focus it is transformed to the pulse with transversal
profile that is similar to the Gaussian one. The effective
ion cumulation region was determined.
The results of the numerical simulation of the ion
cumulation process in plasma located near the lens fo-
cus are presented. Divergence (convergence) of the fo-
cused laser pulse results in a cumulation wave formation
in plasma, which propagates in the direction of the pulse
intensity decrease.
The cumulation coefficient increases when cumula-
tion wave propagates deep into plasma, and maximal
ion energy in the cumulation region decreases. The ob-
tained cumulation coefficient and ion energy values
give the basis for the development of a compact neutron
sources based on a nuclear fusion reaction in effective
ion cumulation region. The main feature of the proposed
neutron source is the removability of the neutron gen-
eration region in plasma volume.
In the focal region, strong defocusing radial and
longitudinal forces influence on ions, that leads to leav-
ing of ions from the focal region and to formation a cav-
ity in plasma.
REFERENCES
1. G.S. Sarkisov, V.Yu. Bychenkov, V.T. Tichonchuk,
et al. // JETP Letters. 1999. v.69, №1, p.20.
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// Problems of Atomic Science and Technology. Se-
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Katse reque
Статья поступила в редакцию 27.05.2008 г.
РАДИАЛЬНОЕ УСКОРЕНИЕ И КУМУЛЯЦИЯ ИОНОВ ПРИ ВЗАИМОДЕЙСТВИИ С ПЛАЗМОЙ
ФОКУСИРУЕМОГО КОЛЬЦЕВОГО ЛАЗЕРНОГО ИМПУЛЬСА
В.А. Балакирев, И.Н. Онищенко, А.И. Поврозин, А.П. Толстолужский, А.М. Егоров
Исследована динамика кумуляции и ускорения ионов дейтериевой плазмы сфокусированным кольцевым
лазерным импульсом фемтосекундной длительности. Определена пространственная структура поля
кольцевого лазерного импульса в окрестности фокуса линзы. Получены значения коэффициента кумуляции
ионов, их энергии и размеры области кумуляции. Сделаны выводы относительно возможности разработки
нейтронного источника, основанного на рассматриваемом принципе кумуляции.
РАДІАЛЬНЕ ПРИСКОРЕННЯ І КУМУЛЯЦІЯ ІОНІВ ПРИ ВЗАЄМОДІЇ З ПЛАЗМОЮ
ФОКУСУЄМОГО КІЛЬЦЕВОГО ЛАЗЕРНОГО ІМПУЛЬСУ
В.А. Балакірєв, І.М. Онищенко, А.І. Поврозін, О.П. Толстолужський, О.М. Єгоров
Досліджена динаміка кумуляції і прискорення іонів дейтерієвої плазми сфокусованим кільцевим
лазерним імпульсом фемтосекундної тривалості. Визначена просторова структура поля кільцевого
лазерного імпульсу поблизу фокуса лінзи. Отримані значення коефіцієнта кумуляції іонів, їх енергії та
розміри області кумуляції. Зроблені висновки відносно можливості розробки нейтронного джерела на
принципі кумуляції, що розглядається.
82
RADIAL ACCELERATION AND CUMULATION OF IONS BY AN INTENSE CONVERGING RING LASER PULSE
INTRODUCTION
REFERENCES
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