Plasma irradiated in a magnetic field

Volume25A. number 8

PHYSICS LETTERS

PLASMA

IRRADIATED

23 October 1967

IN A MAGNETIC

FIELD

A. CAVALIERE, P. GIUPPONI and R. GRATTON Laboratori Gas Ionizatti (Associazione EURATOM-CNEN), Frascati, Rome, Italy Received 15 September 1967

A preliminary theoretical study of a plasma irradiated by a laser, shows that the absorption can be significantly enhanced in an external magnetic field.

P l a s m a s produced by i r r a d i a t i n g solid p a r t i c l e s with l a s e r b e a m s , i f u n d e r g o i n g free i s o t r o p i c expansion, become soon t r a n s p a r e n t and r a p i d l y cool down [1,2]. A m a g n e t i c field b a l a n c i n g the total p l a s m a s t r e s s at an e a r l y stage of e x p a n sion, b e s i d e s t r a n s f o r m i n g p a r t of the r a d i a l e x p a n s i o n e n e r g y back into t h e r m a l energy, can enhance the a b s o r p t i o n through the m o d i f i c a t i o n s of the d y n a m i c s . The high field r e q u i r e d can be a t t a i n e d by allowing a m a g n e t i c flux to be c o m p r e s s e d by the expanding p l a s m a i t s e l f a g a i n s t a hollow m a s s i v e conductor, see fig. 1. In this configuration, heating and expansion p r o c e e d a s in the f r e e i s o t r o p i c [4] case roughly until p > B 2 / 8 ~ , i.e. up to the r a d i u s r * given by: ?

1.7× 10-8A-~W

~/B R}. o2

- I - - - " ? "~-~

I I , I , D ~

\

,

1

!

,

Wabs= 1.01 W

T;1GOeY n : 10~ Cm"~ /

20

1,9

Fig. 2 60

Wltl IO

_ L=IO 100 .s

(1)

(N i s half of total n u m b e r of p a r t i c l e s , W the i n cident power; g a u s s i a n u n i t s a r e g e n e r a l l y used). Henceforth, this i n i t i a l phase shall m e r g e into a second phase, where the expansion m u s t be m a i n l y o n e - d i m e n s i o n a l , and hence can be s e l f r e g u l a t i n g . In fact, were the p r o c e s s a d i a b a t i c , the a b s o r n t i o n coefficient K= 1.4 x × 10 -54 n ~(leT)~ [3] would i n c r e a s e as L; if i n stead r a d i a t i o n s t i l l hits the p l a s m a , an a p p r o x i m a t e b a l a n c e i s conceivably set up between the d e c r e a s e of T due to the expansion and its i n c r e a s e due to the a b s o r p t i o n , so as to m a i n t a i n the p l a s m a above the v e r g e of t r a n s p a r e n c y . The e n e r g y actually a b s o r b e d in this second phase d e pends o n t h e value of 2 K r a i r = r * . Neglecting r a d i a l s t r u c t u r e s , the p r o c e s s can be followed with energy equation :

636

l

Fig. 1. Plasmas expanding in a magnetic field (axial symmetry). Fig.2. Results of the axial model for D (A = 2).

(r*/R)~/[1 - (r*/R)2] 2 = =

i, z~

dT = -3 avz T dr W(t) ~T - ~ - - - ~ 7-~-[ + ~

~-~ x

L

x exp - f K ( z ' ) d z ' + contribution of heat flow . (2) 2 T i s the t e m p e r a t u r e of e l e c t r o n s and ions. Neglecting the i n e r t i a of the r a d i a l motion, it is, in axial approximation, B2oN 4 2nkT- 8~(R2-r2)2 = 0 . (3) This d e s c r i p t i o n is closed by :

dv z / d t = - 2k a ( n T ) / A m p n az , dO~r2)/dt = n r 2 ~v z / a t .

(4) (5)

The r a d i a l d i s p l a c e m e n t of the boundary is a c counted for in eqs. (2), (3) and (5). O r d e r s of magnitude have been computed with

Volume25A, number 8

PHYSICS L E T T E R S

a model where it is assumed a T / a z = 0 a n d v z = z L / L . Then eqs. (2) and (5) can be integrated also along z. Typical results for a plasma assumed [4] initiallydense and in pressure equilibrium with B o are displayed in fig. 2. The corresponding plasma shape at t = 36 × 10 -9 is plotted in fig. 1; note that the axial approximation is poor near the tips [4]. It is seen that the anticipated self-regulation is realized, resulting in an effective absorption of radiation pulses of several tens of nanoseconds, at striking variance with the free-case. Also, during the second phase the density stays roughly constant as the contraction of the radius balances the increase of the length. W e conclude that this configuration substantially affects the absorption through the modifications of the dynamics. At W = 1016, small amounts of plasma (~ 3 x 1017 particles) can be given energay densities in the range of several 1021 e V / c m 3 using pulses lasting many tens of

23 October 1967

n a n o s e c o n d s , without s t r i n g e n t r e q u i r e m e n t s for the r i s e t i m e , the p l a s m a flow r e m a i n s r e a s o n ably steady d u r i n g t i m e s a p p r e c i a b l y l o n g e r than the i r r a d i a t i o n t i m e . We see f r o m eq. (1) that the f i r s t phase leaves the p l a s m a opaque at l e a s t in the r a n g e W ~ N, N -~ 10!6 to 10 l g ' with R 2 × 1 0 -1 a n d B - ~ 5 × 105 . F o r W , N -~1018 , this model would give at t - 10 -7, T -~ 600 eV and v z ~ 108, high enough to r i s e i n t e r e s t in studying the i n t e r a c t i o n s of two such s t r e a m s . D i s c u s s i o n of the a p p r o x i m a t i o n s , and d e v e l o p m e n t s of this work, a r e given in [4]. 1. N.G. Basov and O. M. Krokhin, Soviet Phys. JETP 19 (1964) 123; J.M.Dawson, Phys. Fluids 7 (1964) 981. 2. A. F. Haught and D. H. Polk, UARL E. 920365-4 (1966). 3. H. Hora, IPP report 6/27 (2nd print) (1964) (K for a Nd Laser and Z = 1). 4. A.Cavaliere, P.Giupponi and R.Gratton, LGI 67/11, I and II.

* * * * *

A CONTINUOUSLY TUNABLE, LASER-GENERATED, SOURCE OF RADIATION IN THE 0.5 TO 0.8 MICRON SPECTRAL RANGE* M. D. MARTIN and E. L. THOMAS Ministry of Technology, Signals Research and Development Establishment, Christchurch, Hampshire, UK Received 27 September 1967

A laser-pumped, narrow band (~< 8.0 cm -1) source of radiation with power levels in the kilowatt range and fully tunable from 0.51 to 0.8 microns has been observed.

We wish to r e p o r t the o b s e r v a t i o n of an i n t e n s e , n a r r o w band, s o u r c e of r a d i a t i o n which i s fully tunable over the 0.5 to 0.8 m i c r o n s p e c t r a l region. The o b s e r v e d f r e q u e n c y i s g e n e r a t e d when the output of a Q-switched N d 3 + / g l a s s l a s e r i s propagated as an o r d i n a r y ray n o r m a l to the optic axis, and in the ×z-plane of a LiNbO 3 c r y s tal. The o b s e r v e d tunable frequency has the p o l a r i z a t i o n of an e x t r a o r d i n a r y ray, and the d e pendence of its wavelength on the t e m p e r a t u r e of the IANbO3 c r y s t a l i s shown in figs. 1 and 2.

* This paper is British Crown Copyright and is reproduced with the permission of the Controller of Her Britannic Majesty's Stationery Office.

All the o b s e r v e d f r e q u e n c i e s can be accounted for if it is a s s u m e d that they o r i g i n a t e f r o m u p c o n v e r s i o n p r o c e s s e s of the following type [1] : Wobserved(e-ray) = O~mmp(O-ray) + O~infrared(o-ray) (tunable) (fixed) (tunable) (1) where the fixed pump f r e q u e n c i e s can be e i t h e r the l a s e r (L), the Stokes (S_I) , or the a n t i Stokes (S1) s t i m u l a t e d R a m a n e m i s s i o n involving the 632 cm -1 v i b r a t i o n a l mode of A 1 s y m m e t r y in LiNbO3, [2]. The t h e o r e t i c a l c u r v e s for the t h r e e pump f r e q u e n c i e s , c a l c u l a t e d u s i n g the r e f r a c t i v e index data of Hobden and W a r n e r [3], a r e shown in fig. 2. A g r e e m e n t between the theor e t i c a l c u r v e s and the e x p e r i m e n t a l points ( c r o s ses) i s well within the e x p e r i m e n t a l e r r o r . It 637