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# Plasma physics

Plasma physics is the field of physics which studies ionized gases known as plasmas.

In physics and chemistry, plasma (also called an ionised gas) is an energetic gas-phase state of matter, often referred to as "the fourth state of matter", in which some or all of the electrons in the outer atomic orbitals have become separated from the atom or molecule. The result is a collection of ions and electrons which are no longer bound to each other. Because these particles are ionized (charged), the gas behaves in a different fashion than neutral gas in, for instance, the presence of electromagnetic fields. This state of matter was first identified by Sir William Crookes in 1879, and dubbed "plasma" by Irving Langmuir in 1928.

A common fluid treatment of plasmas comes from a combination of the Navier Stokes Equations of fluid dynamics and Maxwell's equations of electromagnetism. The resulting set of equations, with appropriate approximations, is called Magnetohydrodynamics (or MHD for short).

Plasma physics is important in astrophysics in that many astronomical objects including stars, accretion disks, nebula, and the interstellar medium consist of plasma. It is also important in hypersonic aerodynamics, since at hypersonic speeds the interaction of the shock wave and the boundary layer creates enough heat to ionize the air surrounding a body. This happens, for example, upon re-entry of the Space Shuttle into Earth's atmosphere. Plasma physics is used in work studying nuclear fusion since most known fusion reactions take place in plasma.

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## Characteristics

Plasma is often called the fourth state of matter. It is distinct from the three lower-energy phases of matter; solid, liquid, and gas. Plasmas are the most common form of matter, comprising more than 99% of the known visible universe. Commonly encountered forms of plasma include the Sun and other stars (which are plasmas heated by nuclear fusion), lit fluorescent lamps, lightning, the Aurora borealis, the solar wind, and interstellar nebulae. A plasma is also generated in front of a spacecraft's heat shield on reentering the atmosphere. There is still some debate as to whether plasma is an individual state of matter or simply a type of gas, but most physicists have accepted plasma as a state of matter.

In astrophysical plasmas, Debye screening prevents electric fields from affecting the plasma very much, but the existence of charged particles causes the plasma to generate and be affected by magnetic fields. This can and does cause extremely complex behavior. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of magnetohydrodynamics.

The term plasma is generally reserved for a system of charged particles large enough to behave collectively, excluding microscopically small collections of charged particles. The typical characteristics of a plasma are:

1. Debye screening lengths that are short compared to the physical size of the plasma.
2. Large number of particles within a sphere with a radius of the Debye length.
3. Mean time between collisions usually is long when compared to the period of plasma oscillations.

### Temperatures

The defining characteristic of a plasma is ionization. Although ionization can be caused by UV radiation, energetic particles, or strong electric fields, processes that tend to result in a non-Maxwellian electron distribution function, it is most commonly caused by heating the electrons in such a way that they are close to thermal equilibrium so the electron temperature is relatively well-defined. Because the large mass of the ions relative to the electrons hinders energy transfer, it is possible for the ion temperature to be very different (usually lower).

The degree of ionization is determined by the electron temperature relative to the ionization energy (and more weakly by the density) in accordance with the Saha equation. If only a small fraction of the gas molecules are ionized (for example 1%), then the plasma is said to be a cold plasma, even though the electron temperature is typically several thousand degrees. The ion temperature in a cold plasma is ofter near the ambient temperature. Because the plasmas utilized in plasma technology are typically cold, they are sometimes called technological plasmas. They are often created by using a very high electric field to accelerate electrons, which then ionize the atoms. The electric field is either capacitively or inductively coupled into the gas by means of a plasma source, e.g. microwaves. Common applications of cold plasmas include plasma-enhanced chemical vapor deposition, plasma ion doping , and reactive ion etching.

A hot plasma, on the other hand, is nearly fully ionized. This is what would commonly be known as the "fourth-state of matter". The Sun is an example of a hot plasma. The electrons and ions are more likely to have equal temperatures in a hot plasma, but there can still be significant differences.

### Densities

Next to the temperature, which is of fundamental importance for the very existence of a plasma, the most important property is the density. The word "plasma density" by itself usually refers to the electron density, that is, the number of free electrons per unit volume. The ion density is related to this by the average charge state $\langle Z\rangle$ of the ions through $n_e=\langle Z\rangle n_i$. (See quasineutrality below.) The third important quantity is the density of neutrals n0. In a hot plasma this is small, but may still determine important physics. The degree of ionization is ni / (n0 + ni).

### Potentials

Since plasmas are very good conductors, electric potentials play an important role. The potential as it exists on average in the space between charged particles, independent of the question of how it can be measured, is called the plasma potential or the space potential. If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to the development of a Debye sheath. Due to the good electrical conductivity, the electric fields in plasmas tend to be very small. This results in the important concept of quasineutrality, which says that, on the one hand, it is a very good approximation to assume that the density of negative charges is equal to the density of positive charges ($n_e=\langle Z\rangle n_i$), but that, on the other hand, electric fields can be assumed to exist as needed for the physics at hand.

The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann condition, Failed to parse (unknown function \propto): n_e \propto e^{e\Phi/k_BT_e} . Differentiating this relation provides a means to calculate the electric field from the density: $\vec{E} = (k_BT_e/e)(\nabla n_e/n_e)$.

## Fundamental plasma parameters

All quantities are in Gaussian cgs units except temperature expressed in eV and ion mass expressed in units of the proton mass μ = mi / mp; Z is charge state; k is Boltzmann's constant; K is wavelength; γ is the adiabatic index; ln Λ is the Coulomb logarithm.

### Frequencies

• electron gyrofrequency:
$\omega_{ce} = eB/m_ec = 1.76 \times 10^7 B \mbox{rad/sec}$
• ion gyrofrequency:
$\omega_{ci} = eB/m_ic = 9.58 \times 10^3 Z \mu^{-1} B \mbox{rad/sec}$
• electron plasma frequency:
$\omega_{pe} = (4\pi n_ee^2/m_e)^{1/2} = 5.64 \times 10^4 n_e^{1/2} \mbox{rad/sec}$
• ion plasma frequency:
$\omega_{pe} = (4\pi n_iZ^2e^2/m_i)^{1/2} = 1.32 \times 10^3 Z \mu^{-1/2} n_i^{1/2} \mbox{rad/sec}$
• electron trapping rate
$\nu_{Te} = (eKE/m_e)^{1/2} = 7.26 \times 10^8 K^{1/2} E^{1/2} \mbox{sec}^{-1}$
• ion trapping rate
$\nu_{Ti} = (ZeKE/m_i)^{1/2} = 1.69 \times 10^7 Z^{1/2} K^{1/2} E^{1/2} \mu^{-1/2} \mbox{sec}^{-1}$
• electron collision rate
$\nu_e = 2.91 \times 10^{-6} n_e\,\ln\Lambda\,T_e^{-3/2} \mbox{sec}^{-1}$
• ion collision rate
$\nu_i = 4.80 \times 10^{-8} Z^4 \mu^{-1/2} n_i\,\ln\Lambda\,T_i^{-3/2} \mbox{sec}^{-1}$

### Lengths

• electron deBroglie length
$\lambda\!\!\!\!- = \hbar/(m_ekT_e)^{1/2} = 2.76\times10^{-8}\,T_e^{-1/2}\,\mbox{cm}$
• classical distance of closest approach
$e^2/kT=1.44\times10^{-7}\,T^{-1}\,\mbox{cm}$
$r_e = v_{Te}/\omega_{ce} = 2.38\,T_e^{1/2}B^{-1}\,\mbox{cm}$
$r_i = v_{Ti}/\omega_{ci} = 1.02\times10^2\,\mu^{1/2}Z^{-1}T_i^{1/2}B^{-1}\,\mbox{cm}$
• plasma skin depth
$c/\omega_{pe} = 5.31\times10^5\,n_e^{-1/2}\,\mbox{cm}$
• Debye length
$\lambda_D = (kT/4\pi ne^2)^{1/2} = 7.43\times10^2\,T^{1/2}n^{-1/2}\,\mbox{cm}$

### Velocities

• electron thermal velocity
$v_{Te} = (kT_e/m_e)^{1/2} = 4.19\times10^7\,T_e^{1/2}\,\mbox{cm/sec}$
• ion thermal velocity
$v_{Ti} = (kT_i/m_i)^{1/2} = 9.79\times10^5\,\mu^{-1/2}T_i^{1/2}\,\mbox{cm/sec}$
• ion sound velocity
$c_s = (\gamma ZkT_e/m_i)^{1/2} = 9.79\times10^5\,(\gamma ZT_e/\mu)^{1/2}\,\mbox{cm/sec}$
• Alfven velocity
$v_A = B/(4\pi n_im_i)^{1/2} = 2.18\times10^{11}\,\mu^{-1/2}n_i^{-1/2}B\,\mbox{cm/sec}$

### Dimensionless

• square root of electron/proton mass ratio
$(m_e/m_p)^{1/2} = 2.33\times10^{-2} = 1/42.9$
• number of particles in a Debye sphere
$(4\pi/3)n\lambda_D^3 = 1.72\times10^9\,T^{3/2}n^{-1/2}$
• Alven velocity/speed of light
$v_A/c = 7.28\,\mu^{-1/2}n_i^{-1/2}B$
• electron plasma/gyrofrequency ratio
$\omega_{pe}/\omega_{ce} = 3.21\times10^{-3}\,n_e^{1/2}B^{-1}$
• ion plasma/gyrofrequency ratio
$\omega_{pi}/\omega_{ci} = 0.137\,\mu^{1/2}n_i^{1/2}B^{-1}$
• thermal/magnetic energy ratio
$\beta = 8\pi nkT/B^2 = 4.03\times10^{-11}\,nTB^{-2}$
• magnetic/ion rest energy ratio
$B^2/8\pi n_im_ic^2 = 26.5\,\mu^{-1}n_i^{-1}B^2$

### Miscellaneous

• Bohm diffusion coefficient
$D_B = (ckT/16eB) = 6.25\times10^6\,TB^{-1}\,\mbox{cm}^2/\mbox{sec}$
• transverse Spitzer resistivity
$\eta_\perp = 1.15\times10^{-14}\,Z\,\ln\Lambda\,T^{-3/2}\,\mbox{sec} = 1.03\times10^{-2}\,Z\,\ln\Lambda\,T^{-3/2}\,\Omega\,\mbox{cm}$