Plasma dispersion relation and instabilities in electron velocity distribution function a. The instabilities depend parametrically on the pump wave amplitude and on the plasma beta. Nonlinear magnetoacoustic waves in a cold plasma request pdf. Plasma waves in the fluid picture i max planck society. If the frequency has an imaginary part, that indicates damping or growth of the wave. Properties of possible electrostatic and electromagnetic wave propagation in hot space plasmas can be described by plasma dispersion relation. Publishers pdf, also known as version of record includes final page. We consider electromagnetic waves of the form e e expikr i. It arises in fields like acoustics, electromagnetics, and fluid dynamics historically, the problem of a vibrating string such as that of a musical.
The wave equation is an important secondorder linear partial differential equation for the description of wavesas they occur in classical physicssuch as mechanical waves e. Electromagnetic wave propagation in ionospheric plasma. The cold plasma approximation provides a good description of wave propagation even in quite. Cold relativistic wavebreaking threshold of twodimensional plasma waves j. The considered cold plasma relativistic electron bunch system is interacting with the external monochromatic, linearly polarized electromagnetic em wave, propagating through plasma in x direction and with electric vector directed along z axis p polarization. Cold plasma waves rudolf peierls centre university of oxford. This paper discusses the solution of the cold plasma wave equation for sheath relevant density profiles, e. The equation of electromagnetic wave propagation through cold collisionless plasma can be reduced to the modified kortwegde vries mkdv equation. A bidirectional wave transformation of the cold plasma. To generate the wave equation, we take the curl of eq. In other words, the cold plasma dispersion relation describes waves which either propagate without evanescense, or decay without spatial oscillation. In this paper, we formulate the quaternionic dual fields equations, namely, the hydroelectric and hydromagnetic fields equations which are an analogous to the generalized lamb vector field and vorticity field.
The solutions of the one wave equations will be discussed in the next section, using characteristic lines ct. Cold plasmas transversewaves plasma modifiedlightwaves longitudinal plasma oscillations warmplasmas longitudinalwaves. Wkb approximation for cold plasma waves in the cold plasma waves notes, we assumed that the electromagnetic elds of the wave were of the form e e expikr i. A solid undergraduate background in classical physics, electromagnetic theory including maxwells equations, and mathematical familiarity with partial differential equations and complex. While plasma response should be rigorously derived from the vlasov equation, the situation is greatly simpli. This is actually the dispersion relation of a sound wave propagating along magnetic fieldlines. Request pdf a full wave solver of the maxwells equations in 3d cold plasmas a new solver for maxwells equations in threedimensional 3d plasma configurations is presented. These are transcriptions of the notes from which i teach the single semester course introduction to plasma physics. The twodimensional wave breaking of relativistic plasma waves driven. This means that treating individual particles species. Dispersion in a cold electron plasma ii for vanishing perpendicular electric field, the electrons perform a pure gyromotion.
Under linear superimposition assumption, there is no interaction between these eigen wave. Deriving the fluid equations from the vlasov equation 27 3. A fullwave solver of the maxwells equations in 3d cold. Simpler just to say that all particles of a specific. The asymptotic expansions used in the derivation are also shown as dashed curves. The course is intended only as a first plasma physics course, but includes what i take to be the critical concepts needed for a foundation for further study. Sachs equations for light bundles in a cold plasma 2 signals. On the reflection of electromagnetic waves by a cold magnetoplasma. Asymptotic analysis of the electrostatic wave equation in. The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a. Generation of low frequency plasma waves after wavebreaking. Examples of external forces are the lorentz force and the gravitational force. It is found that plasma gets heated after the wave breaking but a fraction of initial energy always remains with the remnant wave in the form of bgk mode in warm plasma. There are no other waves in cold nonmagnetized plasma.
Thus, in lowplasmas the slow wave is a sound wave modified by the presence of the magnetic field. That wave equation and the associated dispersion relation for the wave modes. Toderivethealfven wave equation weneedfourvector equations. The dual magnetohydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles.
However, the situation changes drastically when a static magnetic eld is imposed. The cold plasma wave equations are solved in the thin region close to a metallic object and a connection coef. The distinction between the fast and slow waves can be further understood by comparing the signs of the wave induced fluctuations in the plasma and magnetic pressures. This is the equation of a harmonic oscillator with the eigenfrequency. The two roots of opposite sign for, corresponding to a particular root for, simply describe waves of the same type propagating, or decaying, in. The antenna is simulated by a constant current sheet in the y direction, intended to preferentially excite the fast wave. Umstadter center for ultrafast optical science, university of michigan, ann arbor, m148109 july 28, 1998 abstract. Assuming a cold plasma means all electrons have the same speed, and thus the current density is simply. There are many mathematical plasma models we have the cold plasma models, i. Some mathematical aspects of wave propagation in the cold. The starting equation is the collisionless boltzmann equation or vlasov equation. Time differentiation yields the driven oscillator equation.
Plasma dispersion relation and instabilities in electron. Generation of low frequency plasma waves after wave. Amplification of external emwave by nonlinear wake waves. The external em wave inside the plasma is described by. Our goal will be to identify the different wave modes that occur in the plasma, and to. Cold plasma finite element wave model for helicon waves. For this treatment, we will regard the plasma as a cold magnetofluid with an associated dielectric constant. A linear perturbation in space plasma can be considered as a linear combination of the eigen wave modes, which can be obtained from the linear wave dispersion relations of the space plasma. Chapter 5 electromagnetic waves in mit opencourseware. A more detailed study of these waves will be a part of a future homework. Can derive the cold plasma approx from fluid plasma equations. In these two examples, and in most other applications to astrophysics, the medium may be modelled as a nonmagnetised pressureless \ cold plasma. Connection coefficients for cold plasma wave propagation.
Some mathematical aspects of wave propagation in the cold plasma model. The wave interaction equations are also studied from the perspective of a single master wave equation, with multiple wave modes, and with a source term due to the entropy wave. Shear alfv en wave the rst one, known as the shear alfv en wave, is xpolarized e y 0 and satis es 1. Chapter 9 waves in cold magnetized plasma anu physics. Surface electromagnetic wave equations in a warm magnetized quantum plasma chunhua li,1 zhengwei wu,1,2,3,a weihong yang,1 and paul k. The type of the envelope equation depends on the characteristics of the original hyperbolic equations, and the speed of the localized wave. The fluid variables before introducing the fluid equations, we need to define fluid variables of plasma. Despite the heroic efforts for which i am very grateful to translate my handwritten materials into latex, and extensive editing on my part, i dont doubt that there are many typographical errors. Cold plasma waves rudolf peierls centre for theoretical physics. On the reflection of electromagnetic waves by a cold.
The starting equation is the collisionless boltzmann equation or vlasov equation for a. This method is applied to the cold plasma equations, in the general case. Spatiotemporal evolution of a nonrelativistic electrostatic waves in a cold plasma has been studied in the wave breaking regime using a 1d particleincell simulation. On the reflection of electromagnetic waves by a cold magnetoplasma citation for published version apa. There are one way wave equations, and the general solution to the two way equation could be done by forming linear combinations of such solutions. The wave is a cold plasma wave when its phase velocity.
One method for investigating the wave breaking limit of a collisionless anisotropic plasma is to employ the warm plasma closure of velocity moments of the 1particle distribution. By examining of the dispersion relation, the types of wave occurred in the media. Mhd analyses that invoke incompressibility typically do so. The equations of motions for the fluctuations read.
Quaternionic approach to dual magnetohydrodynamics of. Vi a it was shown that this equation is mathematically equivalent to the com pressional wave equation v. Also, when wave phase velocities approach thermal velocity of electrons or ions. In this study, because of the cold plasma approximation. Response to comments on alfven resonance reconsidered. Tomori charles university, faculty of mathematics and physics, prague, czech republic. For these reasons, satisfactory description of plasma waves requires kinetic theory. Basic equations let us consider cold collisionless plasma with nonzero background magnetic eld b 0 along the z axis. We write the full coldplasma dispersion relation in terms of the parallel n n sin. We shall first examine the wave types in a cold, magnetized plasma. Lecture notes introduction to plasma physics i nuclear. Chu2 1department of modern physics, university of science and technology of china, 230026 hefei, china 2department of physics and materials science, city university of hong kong, tat chee avenue, kowloon, hong kong 3center of low temperature plasma.
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