Velocity physics1/7/2024 Because this gradient is four orders of magnitude greater than achieved by conventional accelerators (based on fields driven by radio-frequency waves pumped into metal cavities), laser-driven plasma accelerators have received considerable recent attention. This feedback rapidly grows, hence the instability.Ĭorresponding to 1 GeV/cm for n e = 10 18 cm −3. This decreases the density in these regions even further, resulting in more focusing of the laser. Where the laser is more tightly focused, the ponderomotive force will be greater and will tend to expel more electrons. The instability occurs because of how the plasma responds to this. This has the effect of breaking up the laser pulse into a series of shorter pulses of length λ p/2 which will be separated by the plasma period. In the regions of the plasma wave where the plasma density is lower, the radial change in the index of refraction is negative, ∂n( r)/ ∂r 0, the opposite occurs and the laser defocuses. The importance of this lies with how it affects the index of refraction in the plasma. That is, the plasma wave will be three-dimensional in nature with a modulation along the propagation direction of the laser and a decay in the radial direction to the ambient density (see Figure 11). This small plasma wave will have regions of higher and lower density with both longitudinal and radial dependence. Under these conditions, the laser can form a large plasma wave useful for accelerating electrons.Īs the long laser pulse enters the plasma, it will begin to drive a small plasma wave due to either forward Raman scattering or the laser wakefield effect from the front of the laser pulse. Second, the laser must be intense enough for relativistic self-focusing to occur, P > P c, so that the laser can be locally modified by the plasma. First, the laser pulse must be long compared to the plasma wave, L ≫ λ p This allows the Raman instability time to grow, and it allows for feedback from the plasma to the laser pulse to occur. Two conditions must be satisfied for self-modulation to occur in the plasma. In three dimensions, a plasma wave can be driven when transverse self-focusing and stimulated Raman scattering occur together, a process called the self-modulated wakefield instability. The ponderomotive force, due to the beating of the incident and scattered light wave, enhances the density perturbation, creating a plasma wave and the process begins anew. This current then becomes the source term for the wave equation (eqn ), driving the scattered light wave. Energy and momentum must be conserved when the electromagnetic wave ( ω 0, k 0) decays into a plasma wave ( ω p, k p) and another light wave ( ω 0 − ω p, k 0 − k p).įrom an equivalent viewpoint, the process begins with a small density perturbation, Δ n e, which, when coupled with the quiver motion, eqn, drives a current J = Δ n e ev e. When the laser pulse duration is longer than an electron plasma period, τ ≫ τ p = 2 π/ ω p, this photon and electron bunching grows exponentially, leading to the stimulated Raman scattering instability. Local variation in the index of refraction can ‘accelerate’ photons, i.e., shift their frequency, resulting in photon bunching, which in turn bunches the electron density through the ponderomotive force ( F), and so on. The local phase velocity, described in eqns and, can also vary longitudinally if the intensity and/or electron density does. Umstadter, in Encyclopedia of Modern Optics, 2005 Raman Scattering, Plasma Wave Excitation and Electron Acceleration It is calculated from the phase velocity using Eq. When | n p | < 1, phase propagates faster than the speed of light. Given the phase velocity, the phase refractive index n p is the factor describing how much slower the phase is propagating than the speed of light c 0. This relation is generalized to three dimensions in Eq. For this reason, phase velocity is defined as v p = ω / k. This means the quotient on the right is also velocity. The quotient on the left is velocity because it is distance z divided by time t. Rearranging this equation gives z / t = ω / k. For convenience, this constant is chosen to be zero and the argument becomes k z − ω t = 0. The wave moves at a speed that keeps the argument of the sine function a constant. A plane wave traveling in the + z direction can be written as sin k z − ω t. If you were to throw a rock in a body of water and track a point on one of the ripples, you would be observing the phase velocity of the wave. Phase velocity v → p is the speed and direction at which the phase of a wave propagates through space.
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |