On the Stabilization of Explosive Instabilities by Nonlinear Frequency Shifts

Abstract

On the stabilization of explosioe instabilities by nonlinear frequency shifts.

Non-linear reflexion of laser radiation by a plasma layer in a coherent wave description

“…where L = kot and I is the length of the half-period corresponding to Eqs (22), (23). We notice that we furthermore have for the reflexion coefficient W (0) r = X n (0) = W0 (0)…”

“…We may interpret Eq. ( 18) as an equation of motion for a particle with unit mass moving in a potential TT(X 0 , Y) [21][22][23]. The qualitative features of the function n (XQ, Y) are depicted in Fig.…”

“…where y is the reduced damping factor of the longitudinal wave. In the expression (33) we may consider r D as a product where the factor r(L, a) has been weighted by an exponential factor, which has We now have to face the following problem: The reflexion coefficient r is a function of the period ^ of the elliptic solutions (22,23), i.e. r = r ( L , a )…”

Four-Wave Interaction of Positive and Negative Energy Waves in Plasmas

“…We define the growth rate for the explosive instability yexp as the reciprocal of the explosion time so that Consider the situation where al(0) ~' ( 0 ) a3(0) a4(0) # 0 and there is no frequency mismatch. Taking sin e(0) = 0 in (11) without loss of generality, it follows from (10) that I-(' = p2 = p3 = 0 so that ( 14) gives Defining 8 as the energy density of wave 4, then ai = $/a4 so that…”

“…The nonlinear interaction between triplets of positive and negative energy plasma waves and the possible resulting explosive instability has long provided a relevant and fertile field of study for the plasma physicist, e.g., [4][5][6][7][8][9][10][11][12]151. These negative energy waves need a source of available energy in order to propagate and hence are a characteristic feature of beam-plasma systems, plasmas with particle drifts and maser active plasmas.…”