Plasma (an electrified gas with atoms dissociated into positive ions and negative electrons) is often said to be the most abundant form of matter in the universe. The density of a plasma can vary over 28 orders of magnitude – lower density plasmas behave like changing gradient synchrotrons (where single particle trajectories have to be taken into account), while higher density plasmas tend to behave like fluids (movements of individual particles are indifferent) – thus encouraging us to think of plasmas as a 'fourth state of matter'. Most of the matter in the universe is said to exist in the form of a plasma - an electrified gas with positively charged ions and negatively charged electrons.
The left side is the ratio of the number density of the ionized atoms to the neutral atoms in the gas; T is the temperature of the gas in question, Ui the ionization energy, and K the Boltzmann constant. If we plug in the values corresponding to our immediate surroundings, we get an extremely low value for the fractional ionization of the gas, roughly 10 -122. At the same time, however, it is clear that for very high values of T (say millions of degrees), the fraction takes a more.
The latter simply indicates that the movement of particles in one part of a plasma is not only affected by local conditions, but also by the conditions of the plasma in remote regions as well, due to long-range electrodynamic forces. However, if the plasma has a finite temperature, some electrons near the 'edge' of the cloud will have enough thermal energy to cross the potential barrier, thus rendering the shielding incomplete. By 'quasi-neutral' we mean that the electron and ion density in the plasma is more or less equal (so we can refer to a general plasma density n, which appears in the equation above), but not so equal that the electromagnetic forces of interest does not disappear. .
For an ionized gas to qualify as a plasma, we require that the density be high enough that the Debye length is negligible compared to the dimensions of the system L, so that any potential in the plasma is shielded over a relatively short distance . in L, leaving a majority of the plasma without any potential or field.
MAGNETIC MIRRORS
Since the Earth's magnetic field is strong at the poles and weak at the equator, a natural mirror with a rather high Rm value is formed.
PLASMAS AS FLUIDS
The electromagnetic forces (and the collisional term) do not appear in the above equation (as expected), while the viscosity term (the last term on the right-hand side of the above equation) represents the collisional part of the gradient difference of the stress tensor and the pressure gradient in the absence of any magnetic field. One of the reasons the fluid model seems to work for plasma is that the magnetic field can in a sense simulate collisions – restricting the free flow of particles by forcing them to orbit in Larmor orbits. Free flow occurs along the magnetic field, which indicates that the fluid model is not very suitable for movements in this direction.
PLASMA OSCILLATIONS
For example, a plasma with a density of about 1018 m -3, the frequency appears to be close to 9 GHz. The relation above also tells us that the plasma frequency depends only on the plasma density and not k. The group velocity, given by the derivative of the frequency with respect to k, is therefore zero.
THE WEIBEL INSTABILITY – A QUALITATIVE DESCRIPTION
The above explanation of the Weibel instability was presented by Burton Fried, who suggested that the mechanism could be understood in a simple way as the superposition of two or more counter-rotating electron beams.
MATHEMATICAL PARAMETERS – WEIBEL INSTABILITY
SIMULATING THE INSTABILITY
Without loss of generality, we consider the initial velocity distribution ux, uy, uz such that uz is greater than the other two components, which are assumed to be equal. We then consider a perturbation in the y-direction that leads to a Lorentz force that results in a change in the direction of a particle moving along the z-axis, thereby merging the streams into spatially separated sheets (as discussed in the previous section). We assume that the perturbations are exponential in nature, as usual in linear analysis cases.
Next, we use Maxwell's equations, only with the elimination of the transverse displacement current, which corresponds to the neglect of radiation. The inductive effects associated with Faraday's laws are partially retained by the system, which implies that the continuity equations still hold. The linear characteristic size of the computational field is chosen such that the initial anisotropy values correspond to the wavelengths that maximize the growth rate.
The total number of particles must be such that the time frame is sufficient for the instability to develop - however, the calculation costs per simulation also remembered (this appears to be around 106, considering some test runs and theoretical estimates of collision-free time for large particles). Note that the initial value of the energy density is close to zero, which then increases sharply - this corresponds to different areas of current localization. The peak corresponds to the end of the linear step, where the particles become significantly magnetized on average.
The non-linear regime that follows corresponds to a phase where current filaments in similar directions coalesce to form larger structures (this overlaps with a stabilization of the energy density of the magnetic field). Note that regardless of the initial degree of anisotropy, the system saturates to a non-zero threshold value. Our original problem described with appropriate boundary conditions dictates that waves longer than the linear size of the domain cannot exist, which explains the residual anisotropy.
Simply put, this expression means that the fraction of kinetic energy (associated with the z direction) that is ultimately lost to the creation of the Weibel instability cannot exceed 1/6. Moreover, using the dependence of the magnetic energy density on time, and the anisotropy parameter A, the characteristic time of instability can be derived, which can be
CONCLUSION
