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In a Fermi-degenerate plasma, the electronic stopping of a slow ion is smaller than that given by the classical formula, because some transitions between the electron states are forbidden. The bremsstrahlung losses are then smaller, so that the nuclear burning of an aneutronic fuel is more efficient. Consequently, there occurs a parameter regime in which self-burning is possible. Practical obstacles in this regime that must be overcome before net energy can be realized include the compression of the fuel to an ultra dense state and the creation of a hot spot. +

The pondermotive potential in the X-ray Raman compression can generate an electron band gap which suppresses the Landau damping. The regime is identified where a Langmuir wave can be driven without damping in the stimulated Raman compression. It is shown that the partial wave breaking and the frequency detuning due to the trapped particles would be greatly reduced. Coherent intense X-rays might be feasible in near future thanks to the advances in the fields of free electron laser [1,2] and the inertial confinement fusion [3,4]. A short coherent X-ray laser of durations of femto-seconds, would find many applications [5][6][7][8][9]. Even shorter and more intense X-rays would enable probing and manipulating small scale physical processes of ultra-fast time scales. One promising approach for such an ultra short light pulse (even to a few atto-seconds [10,11]) is the backward Raman scattering (BRS), where a pulse gets compressed via laser-plasma interactions. The BRS has already been used to compress the visible light [12]. Recent theoretical analysis has attempted to examine the plausibility of this method in the X-ray regime [10,11].We note that some key physical processes of the X-ray BRS compression in dense plasmas are considerably different from those of the visible light. In particular, due to the short wave length of the pondermotive potential, the quantum diffraction and the degeneracy of the electron states become relevant to the Landau damping and the frequency detuning [13,14]. In this letter, we show that a sufficiently intense wave modifies the electron's momentum energy dispersion relation and forms an electron band structure, by which the Landau damping gets suppressed [15]. We also show that the wave breaking via the trapped electrons gets considerably reduced.Consider a wave in the form of φ(x, t) = eφ 0 cos(kx − ωt). The classical analysis of the Landau damping rate, γ cl , for small eφ 0 shows that [15]where k (ω) is the wave vector (frequency), ω pe = (4πn e e 2 /m e ) 1/2 is the plasma frequency, and f is the electron distribution function with the normalization condition f d 3 v = 1. The damping rate γ can be alternatively derived from the dielectric function formalism: * Electronic address: sku@cims.nyu.eduwhere ǫ is the well-known dielectric function obtained by the random phase approximation. For high k values comparable to the electron de Broglie wave length, the dielectric function should be replaced by the Lindhard function [16]:where E(v i ) (E(v f )) is the electron energy whose momentum is m e v i = m e v − k/2 (m e v f = m e v + k/2). The imaginary part of the dielectric function is given from Eq. (3) as [17](4) In the limit ∼ = 0, Eq. (4) is reduced to Eq. (1). Eq. (4) describes a process an electron with v = v i absorbs quanta from the wave and transitions to the state with v = v f while the total energy ( ω = E f − E i ) is conserved. The Landau damping can be understood more clearly in the co-moving reference frame where the wave is stationary: y = x − (ω/k)t. In this reference f...

Experimentally observed decay rate of the long wavelength Langmuir wave in metals and dense plasmas is orders of magnitude larger than the prediction of the prevalent Landau damping theory. The discrepancy is explored, and the existence of a regime where the forward Raman scattering is stable and the backward Raman scattering is unstable is examined. The amplification of an x-ray pulse in this regime, via the backward Raman compression, is computationally demonstrated, and the optimal pulse duration and intensity is estimated.PACS numbers: 52.38.-r, 52.59. Ye, 42.60.Jf Coherent intense x-rays would enable various potential applications [1,2], however, it is very difficult to compress an x-ray pulse, or even in the UV regime. Some progress has been made in this direction, based on the recent advances in the areas of free electron laser [3] and the inertial confinement fusion [4]. It is shown that the backward Raman scattering (BRS) [5,6], where two light pulses and a Langmuir wave interact one another to exchange the energy, is one promising approach to create an ultra short light pulse (down to a few attoseconds [7,8]); a pulse gets compressed and intensified via this laser-plasma interaction. The BRS is successfully used to create intense pulses of the visible light frequencies [9,10]. It is natural to consider the same technique for the x-ray compression [7,8]. However, some physical processes in the regime where x-rays might be compressible are considerably different from those in the visible light regime. There are new physical processes to be considered, such as the Fermi degeneracy and the electron quantum diffraction [11][12][13][14], to mention a few.We consider one key aspect for the BRS in the x-ray compression regime, i.e., the damping of the Langmuir wave. In an ideal plasma, the decay rate of the Langmuir wave increases rapidly as the wavelength decreases. It poses a concern for the BRS, as the plasmon from the forward Raman scattering (FRS), having a lower wave vector than the BRS, depletes the pump. There have been various attempts to suppress the FRS in the visible light regime [15]. The situation is different in metals and the warm dense matters that we consider for the x-ray compression. The interaction of electrons via the inter-band transition (the Umklapp process) [16][17][18][19][20][21][22] becomes the dominant plasmon decay process, in contrast to the Landau damping in an ideal plasma. As a consequence, the decay rate of the long wavelength plasmon * Electronic address: seunghyeonson@gmail.com † Electronic address: sku@cims.nyu.edu ‡ Current address: Citigroup, 388 Greenwich St. New York, NY 10013 is much higher than the prediction of the prevalent dielectric function theory. In this paper, we show that a parameter regime where the BRS is unstable and the FRS is stable does exist in metals and warm dense matters, as the plasmon from the FRS strongly decays. Here, we consider metals in room temperature, and show that an x-ray pulse can be compressed in this regime. We estimate an optima...