Plasma temperature and density are key parameters that define a plasma's behavior. They determine how particles move, interact, and respond to external forces. Understanding these concepts is crucial for characterizing different types of plasmas and their properties.

Electron and ion temperatures, often different, are measured in energy units. Plasma density varies widely across different environments. These parameters influence important plasma characteristics like thermal velocity, degree of ionization, and plasma beta, which affect plasma behavior and confinement.

Plasma Temperatures

Electron and Ion Temperature Characteristics

• Electron temperature measures average kinetic energy of electrons in plasma
• Ion temperature quantifies average kinetic energy of ions in plasma
• Temperatures expressed in units of energy (eV) or Kelvin (K)
• Conversion between eV and K follows relationship: 1 eV ≈ 11,600 K
• Plasma often exhibits different electron and ion temperatures
  • Electrons typically heat faster due to lower mass
  • Temperature equilibration occurs through collisions

Temperature Anisotropy and Thermal Velocity

• Temperature anisotropy arises when particle velocities differ in various directions
• Occurs in magnetized plasmas due to particle motion constraints along field lines
• Perpendicular temperature (T⊥) differs from parallel temperature (T∥)
• Anisotropy ratio defined as A = T⊥ / T∥
• Thermal velocity represents average speed of particles in plasma
• Calculated using formula: $v_{th} = \sqrt{\frac{2k_BT}{m}}$
  • kB represents Boltzmann constant
  • T denotes temperature
  • m signifies particle mass
• Thermal velocity differs for electrons and ions due to mass difference

Plasma Density and Ionization

Plasma Density Measurements

• Plasma density refers to number of charged particles per unit volume
• Typically measured in particles per cubic meter (m^-3)
• Electron density (ne) often equals ion density (ni) in quasineutral plasmas
• Density ranges vary widely across different plasma types
  • Low-density plasmas (interstellar medium): ~10^6 m^-3
  • High-density plasmas (fusion experiments): ~10^20 m^-3
• Debye length relates to plasma density, determines electrostatic shielding distance

Degree of Ionization and its Implications

• Degree of ionization measures fraction of atoms that are ionized in plasma
• Calculated as ratio of electron density to total particle density
• Ranges from weakly ionized (< 1%) to fully ionized (100%)
• Affects plasma properties and behavior
  • Higher ionization leads to increased conductivity
  • Influences collision frequencies between charged and neutral particles
• Saha equation describes ionization degree in thermal equilibrium plasmas
• Factors influencing ionization degree include temperature, pressure, and atomic properties

Plasma Distribution and Parameters

Maxwellian Distribution in Plasma Physics

• Maxwellian distribution describes velocity distribution of particles in thermal equilibrium
• Represents probability of finding particles with specific velocities
• Three-dimensional Maxwellian distribution function given by: $f(v) = n(\frac{m}{2\pi k_BT})^{3/2} \exp(-\frac{mv^2}{2k_BT})$
• Characterizes many plasma systems, particularly those in thermal equilibrium
• Deviations from Maxwellian distribution occur in non-equilibrium plasmas
  • Presence of electric fields
  • Wave-particle interactions
  • Particle injection or loss mechanisms

Plasma Beta and its Significance

• Plasma beta (β) measures ratio of plasma pressure to magnetic pressure
• Defined as $\beta = \frac{n k_B T}{B^2 / 2\mu_0}$
  • n represents plasma density
  • T denotes temperature
  • B signifies magnetic field strength
  • μ0 represents permeability of free space
• Indicates relative importance of thermal and magnetic effects in plasma
• β > 1: Plasma pressure dominates (plasma confinement challenging)
• β < 1: Magnetic pressure dominates (easier plasma confinement)
• Varies across different plasma environments
  • Solar corona: β ~ 0.1
  • Tokamak fusion devices: β ~ 0.05
• Crucial parameter in plasma confinement and stability analysis