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CO2 laser induced compton effect in underdense hydrogen plasma
Volume 42A, number 7
PHYSICS LETTERS
29 January 1973
CO2 LASER INDUCED COMPTON EFFECT IN UNDERDENSE HYDROGEN PLASMA A.A. OFFENBERGER and N.H. BURNETT Department of Electrical Engineering, The University of Alberta, Edmonton, Canada Received 20 November 1972
Recent experimental observation of induced scattering of CO2 laser radiation by an underdense hydrogen plasma can be explained theoretically by non-linear and Compton scattering from ions in the highly cooperative plasma conditions prevailing (k XD ~ 1).
Experimental observation of stimulated Compton scattering of high intensity CO2 laser radiation by and underdense plasma has been reported [1]. Measured shifts of the spectrum of transmitted radiation showed poor agreement with the theory of induced scatteringby free electrons according to Peyraud [2]. Recently Babuel-Peyrissac [31,using the theory of Tsytovich [4] has shown that induced scattering could explain a Stokes shift in a neody. nium laser-plasma experiment [5] if account is taken of the dressed ions in a highly cooperative regime (k XD ~ This theory is also applicable to our case and shows good agreement with experiment [1]. Scattering of photons of wave number k’ into wave number k satisfies the following equation [4] 1 dNk dudk’ (k—k’) ~f w10~~~ ~ Nk’ ~
-~--
~
where the ion scatteringprobability 3e4 [1 + (k~k’)2] I ö[~—w’—(k—k’) u] k2k2 J(1+7/1)2 Wion = 2m~ww (2ir) under conditions discussed by the above authors and which are satisfied for the present experiment. With the assumption of a Maxwellian velocity distribution and mean values for the scattering angle, integration over velocity space gives
‘fk = where
—
a2
2 3~ (2ir)
r~c2n (xT~)k~fdk’(k’_k) exp [—a2(k’—k)2] Nk’ 0ha
2/mec2 0= e Finally assuming a Gaussian laser spectrum of width 1 for convenience =
mic2/8(X7)k~ sinf 0,
r
—
though Lorentzian would be more accurate
Nk’ = (2ir)3 NT1 exp [_12 (k’—k 2J/~.Fk’2~ 0) where NT = I/h~.,c,integration over k’ yields = 2 r~n 2 0I I a! (k—k0) exp ~2l2 (k—k0) v’~(xT 2 (a2+12)3/2 La2+12
[
1)k~(l+T~,ITi)
Consequently, the shift will occur for that L~Jc= k—k
7k
which is
0 maximizing =
k—k
2 + 12/2a212)112 0
=
(a 527
—
Volume 42A, number 7
with a corresponding growth rate /~ r~n~I 212+ 12) ‘Vmax = \/~ (xT~)k~(a
PHYSICS LETTERS
(1 +
29 January 1973
1TelTi)2
For the experimental conditions given in ref. [1], no = 1018 cm3, 77~ = 10 eV, 12 = 452 cm1, a2 20 cm1 the calculated shift &~= 2.9A and ‘Vm~= 7 X 108 sec1. The measured shift was 3.2A which shows good agreement with the calculated value. In order to have significant scattering occur the interaction time r given by d/c where d = average plasma dimension (1 cm), must be of the order of y1. For the two pass transmitted radiation r ‘\‘ 10—10 sec which agrees within one order of magnitude to ‘y1. In view of the approximations made in the foregoing derivation, the agreement can be considered adequate. From the growth rate expression for ‘y the rate of scattering photons varies as X3 which points out the obvious advantage of using lOj.z radiation for these investigations. =
References Eli
N.H. Burnett, R.D. Kerr and A.A. Offenberger, Opt. Comm. to be published. 12] J. Peyraud, J. de Physique 29 (1968) 88; 29 (1968) 306. 3] J.P. Babuel-Peyrissac, Phys. Lett. 41A (1972) 143. 14] V.N. Tsytovich, Nonlinear Effects in Plasmas (Plenum Press, New York, 1970). 151 M. Decroisette, G. Piar and F. Floux, Phys. Lett. 32A (1970) 249.
528
PHYSICS LETTERS
29 January 1973
CO2 LASER INDUCED COMPTON EFFECT IN UNDERDENSE HYDROGEN PLASMA A.A. OFFENBERGER and N.H. BURNETT Department of Electrical Engineering, The University of Alberta, Edmonton, Canada Received 20 November 1972
Recent experimental observation of induced scattering of CO2 laser radiation by an underdense hydrogen plasma can be explained theoretically by non-linear and Compton scattering from ions in the highly cooperative plasma conditions prevailing (k XD ~ 1).
Experimental observation of stimulated Compton scattering of high intensity CO2 laser radiation by and underdense plasma has been reported [1]. Measured shifts of the spectrum of transmitted radiation showed poor agreement with the theory of induced scatteringby free electrons according to Peyraud [2]. Recently Babuel-Peyrissac [31,using the theory of Tsytovich [4] has shown that induced scattering could explain a Stokes shift in a neody. nium laser-plasma experiment [5] if account is taken of the dressed ions in a highly cooperative regime (k XD ~ This theory is also applicable to our case and shows good agreement with experiment [1]. Scattering of photons of wave number k’ into wave number k satisfies the following equation [4] 1 dNk dudk’ (k—k’) ~f w10~~~ ~ Nk’ ~
-~--
~
where the ion scatteringprobability 3e4 [1 + (k~k’)2] I ö[~—w’—(k—k’) u] k2k2 J(1+7/1)2 Wion = 2m~ww (2ir) under conditions discussed by the above authors and which are satisfied for the present experiment. With the assumption of a Maxwellian velocity distribution and mean values for the scattering angle, integration over velocity space gives
‘fk = where
—
a2
2 3~ (2ir)
r~c2n (xT~)k~fdk’(k’_k) exp [—a2(k’—k)2] Nk’ 0ha
2/mec2 0= e Finally assuming a Gaussian laser spectrum of width 1 for convenience =
mic2/8(X7)k~ sinf 0,
r
—
though Lorentzian would be more accurate
Nk’ = (2ir)3 NT1 exp [_12 (k’—k 2J/~.Fk’2~ 0) where NT = I/h~.,c,integration over k’ yields = 2 r~n 2 0I I a! (k—k0) exp ~2l2 (k—k0) v’~(xT 2 (a2+12)3/2 La2+12
[
1)k~(l+T~,ITi)
Consequently, the shift will occur for that L~Jc= k—k
7k
which is
0 maximizing =
k—k
2 + 12/2a212)112 0
=
(a 527
—
Volume 42A, number 7
with a corresponding growth rate /~ r~n~I 212+ 12) ‘Vmax = \/~ (xT~)k~(a
PHYSICS LETTERS
(1 +
29 January 1973
1TelTi)2
For the experimental conditions given in ref. [1], no = 1018 cm3, 77~ = 10 eV, 12 = 452 cm1, a2 20 cm1 the calculated shift &~= 2.9A and ‘Vm~= 7 X 108 sec1. The measured shift was 3.2A which shows good agreement with the calculated value. In order to have significant scattering occur the interaction time r given by d/c where d = average plasma dimension (1 cm), must be of the order of y1. For the two pass transmitted radiation r ‘\‘ 10—10 sec which agrees within one order of magnitude to ‘y1. In view of the approximations made in the foregoing derivation, the agreement can be considered adequate. From the growth rate expression for ‘y the rate of scattering photons varies as X3 which points out the obvious advantage of using lOj.z radiation for these investigations. =
References Eli
N.H. Burnett, R.D. Kerr and A.A. Offenberger, Opt. Comm. to be published. 12] J. Peyraud, J. de Physique 29 (1968) 88; 29 (1968) 306. 3] J.P. Babuel-Peyrissac, Phys. Lett. 41A (1972) 143. 14] V.N. Tsytovich, Nonlinear Effects in Plasmas (Plenum Press, New York, 1970). 151 M. Decroisette, G. Piar and F. Floux, Phys. Lett. 32A (1970) 249.
528