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Submitted on 1 Jan 1979
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THE DYNAMICS OF A HIGH-FREQUENCY DISCHARGE IN A WAVE BEAM
V. Gil’Denburg, A. Litvak, A. Yunakovsky
To cite this version:
V. Gil’Denburg, A. Litvak, A. Yunakovsky. THE DYNAMICS OF A HIGH-FREQUENCY DIS- CHARGE IN A WAVE BEAM. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-215-C7-216.
�10.1051/jphyscol:19797106�. �jpa-00219076�
JOURNAL DE PHYSIQUE CoZZoque C7, supptbment au no?, Tome 40, JuiZZet 1979, page C7- 215
M E DYNAMICS OF A HIGH-FREQUENCY DISCHARGE IN A WAVE BEAM
V.B. Gilldenburg, A.G. Litvak and A.D. Yunakovsky.
Applied Physics Institute, Academy of Sciences of the U. S . S.R., Gorky-U!S. S. R.
m e of the inportant problems in tke
t
-L\/ag
(radial coordinate), 2- 2/Lo theory of a high-frequency discharge in (longitudinal coordinate),n- n /no
electroma@;netic wave beams (optical [I]
,
(electron density) asing the following 2submillimeter [2] and rf [3] bands) is designations:
a.
andto- k
Qo m e thethe study of self-consistent plasma-fwd characteristic transveree and longitu- evolution at the first afterbreakdom st*
gee charactprized by high electron tempe- 4 O
rature (T,
>
10 K) and low heavy parti- cle temperature ( T m ~ 300°K). In the pre- sent paper the computer simulation results for the dynamics of euch a noneqailibrium discharge in a converging wave beam are given. The analogous problem for a diver- ging beam was solved in [4].
!the ionization by an electron impact (with frequency Qi ) and attachment to molecules (with frequency
&
were as-sumed to be the main proceases responsible for electron balance. The frequency dif- f erence
$, -
was cons ldered as the gi- ven function of the field amplitudeH e r I const; Ec is the breakdown am- plitude, The plaama diffusion was assumed unessential for the discharge scales a8
8 whole but strong enough to suppress mall-scale ionization instability [6]
,
Under these assumptions the electric ba- l a c e equation
was solved together with the perabolic equation for a walovP field amplitude of the axissnrmetric ~araxial beam
Equations (21, (3) art written in dimen- sionles. variables:
1-3 a t ' E- E/ Ec ,
dinal scales of an unperturbed beam rcs- pectively
(kao>>>l),
k=to/c,
is the field frequency, no= 2 2
a/k to , n,=m(w +3 )/4rt e2
is the critical dell- rfty,3
is the electron collisional frequency,n,
ie the initial density defined by the intensity of an-external ionizer,l = $ a b o / ~
is the electro-magnetic eignal delay parameter, Parabolic equation (3 ) holding when the sonditiona
k
Po>>, n << kto
are uatisfied describes diffraction, refraction and absorption of a beam.
The boundary conditions for equa- tions (21, ( 3 ) are given based upon the fact that the unperturbed beam ie Gaus-
sian and focused at the distance Zg from the boundary
Em is the field at the centre of the focal apot. Far enough from the axis ( "t a 6) it was assumed that E = 0.
!Che initial conditiona are:n (t = 0)
,
=
n,
I const; E(t = O)=E1(*t,Z ), whe- re El is the solution ofeq,(3) with thegiven boundary conditions for
n = n
7 so.
I'
Numerical calculations were made for the values of the parameters
and for three values of parameter
$/u:O
0.02 and 3. The 3-layer ll-pointwhsme
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797106
of the higher order of accuracy was used.
Thescheme parameters were chosen in such a way that when integrating over the cha- racteriat ic
k= Z-t
the phase ratios were correct, The results are shown in Fig.1 as the plots of radial &d axial distributions of densityn
and field amplitude(€1
for different values of time
t .
As it ia seen, a rapid (avalenche- -type) initial growth of the denaity for
tw{
stops due to the decrease of the field amplitude and the ionization maximum be- gins to propagate from the focus towards the lens (breakdown wave). For suff icien- tly larget
the rates of the discharge evolution etrongly decrease and the field value exceeding the "breakdownu one beco- mes small (in qualitative agreement with the stationary model aeeumption [7] 1. For m a l l$10
aiter the first ionization ma- ximum there occur secondary ones which are weaker and practically stop for larget .
For
$10.
3 (in this case the beam refrac- tion in unessential and the field dynamics ia defined by absorption) the discharge quickly approaches the stationary state.Radial profiles of density
n
( ^t ) and fieldIEl
( '% ) are alwayw monotono- ue for$/a
= 3. For a small$ 1 ~
there aregaps on the axis for eome
t
andZ .
Based upon a qualitative analysis of eqa.(2), (3) which agree with numerical reaults obtained it is not difficult to show that the first maximum of electron density is of the order of magnitude (in dimenaion.ese variables )
n - 00 4
(5)9 G n -, n - n,
nrnax
"4(ka3t'
so that for sufficiently large
k
Qo the initial assumptionn <<n
is satisfiedmax
ceven for
\)
= 0 and rather smalln, .
It should be emphasized that this result is correct only in the absence of small scale instability [6]
,
which makes the discharge evolution more complicated and result8 in its decay into clusters with densityn
NnC .
References
1. Yu.P.Raizer. Laser Spark snd Dischar- ge Propogation. "Naykan, 1974.
2. P.Woskoboinikow, W.T.?dulligan,
H.C.Fraddaude. D.R.Cohnr A~~l.Phus.
- -
Lett.,
32,
52?, 1978.3. A.V.Gurevich. Geomagn.Aeron,
12,
631, 1972.5. A.D.~cDonald. Microwave Breakdown in Gases, J.Wiley, New York, 1966.
6 , V.D.Gil'denburg, A.V.Kim, ZhETF,
2,
141. 1978.
7. ~ . ~ ; ~ i i i denburg, S.V.Golubev, ZhETF,
