Growth Rate Of Parametric Instability Research Articles

Wave Processes in Rotating Compressible Astrophysical Plasma Flows with Stable Stratification

The wave processes in a rotating layer of compressible astrophysical plasma with a stable stratification and a linear entropy profile are studied theoretically. The compressibility is taken into account in the anelastic approximation. In this approximation the acoustic waves are filtered out, the system contains terms with a potential temperature (entropy), and the continuity equation contains an initial stratified density profile. The Coriolis force in the magnetohydrodynamic equations for a compressible astrophysical plasma is considered in four different approximations: a traditional f-plane, a nontraditional f-plane (given the horizontal component of the Coriolis force), a traditional β-plane, and a nontraditional β-plane. Linear and nonlinear theories of wave processes have been developed for each Coriolis force approximation under consideration. New types of waves have been found, with the rotation, magnetic field, gravity, and compressibility serving as their restoring mechanisms. The compressibility effects are represented in the new dispersion equations by the Brunt–Vaisala frequency for compressible stratified flows dependent on both initial density and pressure profiles. All of the realizable types of three-wave interactions have been revealed through a qualitative analysis of the dispersion curves. A system of equations for the amplitudes of interacting waves and the growth rates of parametric instabilities have been derived by the multiscale expansion method.

Experimental and theoretical study of secondary acoustic instability of downward propagating flames: Higher modes and growth rates

Flames propagating in tubes open at the ignition end typically show two different kinds of thermo-acoustic instability namely, primary and secondary. Secondary acoustic instability is accompanied by parametric instability of flame front during which, cellular structures on the flame surface oscillate with half the acoustic frequency of excitation. The growth rates associated with secondary acoustic instability of flame structure are higher compared to primary instability of flames leading to very high peak pressures. In this work, we present experimental and theoretical study on parametric instability of downward propagating C2H4/O2/CO2 flames at two different Le of 1.0 and 0.8. Lower Le mixtures are found to be more unstable. Parametric instability of higher acoustic modes is reported for the first time for gaseous fuels. Higher modes of parametric instability transitioned successively to lower modes as the flame propagated downward. Growth rate of parametric instability is measured in experiments. Theoretical prediction of growth rate is done based on velocity coupling mechanism. Theoretical calculations provide good approximation of growth rates and its variation with frequency.

Parametric excitation of surface ion cyclotron extraordinary polarized waves by an external alternating electric field

An external alternating electric field in the range of ion–cyclotron frequencies is shown to excite extraordinary polarized surface electromagnetic waves at the second harmonic of ion–cyclotron frequencies. The kinetic model of a uniform semi-bounded plasma is applied. Plasma electrodynamical properties are described by using the Vlasov–Boltzmann kinetic equation in the approach of weak spatial plasma dispersion. Two components of these modes’ wave vector, which are oriented across an external steady magnetic field, are taken into account. Fields of these ion–cyclotron modes are described by Maxwell equations. Their phase velocity is assumed to be much lower than light velocity. The external alternating electric field is assumed to be uniform and monochromatic. The nonlinear boundary condition is formulated for the tangential magnetic field of the studied surface waves (SW). An infinite set of equations is derived for the values of tangential electric field harmonics on the plasma interface. This set is solved using the approach to the wave packet consisting of the main harmonic and two nearest satellite harmonics. Simple analytical expressions for the growth rates of parametric instability of these SW are derived. The influence of plasma parameters on their parametric excitation is numerically analyzed.

Linear baroclinic and parametric instabilities of boundary currents

The linear baroclinic and parametric instabilities of boundary currents with piecewise-constant potential vorticity are studied in a two-layer quasi-geostrophic model. The growth rates of both the exponential modes and of the optimal perturbations are calculated for the baroclinic instability of steady coastal currents. We show that the growth rates of the exponential modes are maximal for a vertically symmetric flow. Furthermore, the vertical asymmetries induced by different layer thicknesses, the presence of a barotropic potential vorticity or bottom topography, all act to dampen the growth rates and favor growth at shorter wavelengths. It is shown that this behavior can be predicted from the conditions for vertical resonance of Rossby waves on the two potential vorticity fronts. Also, the baroclinic instability of the optimal perturbations has larger growth rates at shorter wavelengths and shorter time scales. As well, the presence of a sloping bottom of moderate amplitude favors the growth of these optimal perturbations. Finally, we compute the growth rates of parametric instability of oscillatory coastal flows. We show that subharmonic resonance is the most unstable mode of growth. In addition, a second region of parametric instability is found (for the first time) away from marginality of exponential-mode baroclinic instability. It is shown that the functional dependency of the growth rates of parametric instability, for optimal excitation, are similar to that of the optimal perturbations of baroclinic instability. To explain this a mechanism for parametric instability, involving the rapid growth of short-wave optimal perturbations, is proposed.

Numerical investigations and analysis on the effects of geometrical parameters on the group velocity of transverse magnetic pump mode and free electron laser instability

In this paper, we have numerically investigated the effects of various geometrical parameters of a backward wave oscillator, filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate R0 of a seeded free electron laser. On changing mean radius corrugation amplitude h and corrugation period z0 of backward wave oscillator; the ponderomotive potential of space charge wave changes. This in turn, changes the coupling strength of TM mode with negative beam space charge mode and hence the growth rate of parametric instability of free electron laser. A dispersion relation is derived and numerically solved for various geometrical parameters of backward wave oscillator and beam profile. A relation for Γ is also derived and computed numerically. The instability growth scales directly to the square root of beam density and inversely as seven power of relativistic gamma factor γ0.

Spectral broadening of lower hybrid waves produced by parametric instability in current drive experiments of tokamak plasmas

In order to explain the results of the non-inductive current produced in the lower hybrid current drive (LHCD) experiments, a broadening of the radiofrequency (RF) power spectrum coupled to tokamak plasma needs to occur. The presented modelling, supported by diagnostic measurements, shows that the parametric instability (PI) driven by ion sound quasimodes, which occur in the scrape-off plasma layer located near the antenna mouth, produces a significant broadening of the launched LH spectrum. Considering the parameters of LHCD experiments of JET (Joint European Torus), and other machines as well, the PI growth rate is high enough for producing the compensation of the convective losses and, consequently, the broadening of a small fraction (of the order of 10%) of the launched power spectrum. Such a phenomenon is identified to be intrinsic to the RF power coupling in the LHCD experiments. As the principal implication of considering such spectral broadening in modelling the LH deposition profile, experiments of LHCD-sustained internal transport barriers in JET were successfully interpreted, which evidenced the effects of a well-defined LH deposition profile. The present work is important for addressing the long-lasting debate on the problem of the so-called spectral gap in LHCD. The design of LHCD scenarios relevant to the modern fusion research programme, an important requirement of which is the control of the plasma current profile in the outer half of plasma, can be properly achieved by considering PI-induced spectral broadening.

Suppression of convective cell generation by Alfvén waves in the ionospheric auroral cavity

A theory for the parametric interaction of inertial Alfvén wave (IAW) packets with large-scale convective cells accounting for the nonzero ratio of the Alfvén and light velocities is presented. It is shown that in the auroral plasma cavity where the Alfvén velocity has its maximum value, the parametric interaction of IAWs with convective cells is substantially reduced. In this region the Alfvén velocity is comparable to the speed of light and thus the displacement current cannot be neglected. This current plays a stabilizing role and results in a decline of the parametric instability growth rate. On the contrary, the incorporation of the finite width of the IAW packet leads to increase in the convective cell growth rate. A compact expression for the instability growth rate and the optimal conditions for the fastest growing convective mode are derived. The relevance of the theory to recent spacecraft measurements in the Earth’s ionosphere is pointed out.

Influence of absorption and refraction on laser interaction studies in preformed plasmas

We report on a numerical and experimental study of the propagation of a laser beam in a performed plasma. The physical parameters concerning the laser and the plasma are those of an experiment described in the Proc. 16 European Conf. on Controlled fusion and plasma physics, 1989, p. 837. The stationary electron density profile is provided by hydrodynamic simulations. We show that refraction is important for plasma densities related to a critical density ( n e/ n c) higher than 0.1. The main consequence is the variation of the spatial laser intensity distribution inside the plasma and the lowering of the interaction length which can, consequently, modify thresholds and growth rates of parametric instabilities. We also show that a transverse depression in the plasma density, which could be due to filamentation of the interaction beam, can modify the angular diagram of the transmission.

Growth rates of parametric instabilities driven by two pumps

The parametric instability growth rate of ion-acoustic and Langmuir waves, driven unstable by two uniform pumps near the Bohm–Gross frequency, is calculated as a function of pump amplitudes and frequencies. Two instability mechanisms can be identified: one corresponds to the usual, single pump parametric instabilities (decay and oscillating two stream), while the other is similar to that found in the Mathieu equation. The interaction between these two mechanisms results in a nonmonotonic dependence of the growth rate on the pump amplitudes and frequencies: both cancellation and enhancement are obtained for various values of the parameters. An analytic study of the relevant dispersion relation using Hill’s method is complemented by numerical studies in both the frequency and time domains.

Study of short wavelength instabilities the confinement of a collision dominated plasma by a rotating magnetic field

A collision dominated plasma confined by a rotating magnetic field is stable if f>or approximately=0.02 vi where f is the frequency of rotation and vi the ion collision frequency. Short wavelength perturbations are the most difficult ones to stabilize. Growth rates of parametric instabilities are shown to be so large as to make impossible any attempt to use a frequency much lower than the above limit. A simple interpretation of a wide region of instability, which cannot be ascribed to any parametric instability, is given in terms of an equivalent negative resistance.