2.2 Plasma Kinetics and Thermodynamics

Plasma kinetics and thermodynamics are crucial for understanding plasma behavior. Temperature measures average particle energy, while the Maxwell-Boltzmann distribution describes velocity probabilities. These concepts help explain how particles move and interact in plasmas.

Energy transfer in plasmas occurs through collisions and radiation. Thermodynamic laws govern plasma equilibrium, balancing energy gain and loss. Understanding these principles is essential for predicting and controlling plasma behavior in various applications.

Plasma Kinetics

Plasma temperature and kinetic energy

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• Plasma temperature measures the average kinetic energy of particles in a plasma expressed in electron volts (eV) or Kelvin (K)
• Kinetic energy of a particle is given by $E_k = \frac{1}{2}mv^2$ where $m$ is the particle mass and $v$ is its velocity
• Average kinetic energy per particle in a plasma is $\bar{E_k} = \frac{3}{2}k_BT$ where $k_B$ is the Boltzmann constant and $T$ is the plasma temperature
• Higher plasma temperature indicates higher average particle velocities (electrons, ions)
• Particle velocity distribution in a plasma depends on the plasma temperature (Maxwell-Boltzmann distribution)

Maxwell-Boltzmann distribution in plasmas

• Maxwell-Boltzmann distribution is a probability distribution function for particle velocities in a plasma at thermal equilibrium
• Describes the likelihood of a particle having a specific velocity at a given temperature
• Derivation steps:
  1. Consider a system of particles in thermal equilibrium
  2. Apply the Boltzmann distribution for energy states
  3. Relate the energy states to particle velocities
  4. Normalize the distribution to ensure the total probability equals 1
• Resulting distribution function: $f(v) = 4\pi \left(\frac{m}{2\pi k_BT}\right)^{3/2} v^2 \exp\left(-\frac{mv^2}{2k_BT}\right)$ where $f(v)$ is the probability density function for particle velocities, $m$ is the particle mass, and $v$ is the particle velocity

Plasma Thermodynamics

Energy transfer in plasmas

• Collisional energy transfer occurs through elastic and inelastic collisions
  • Elastic collisions involve kinetic energy exchange between particles (electrons, ions) and maintain overall kinetic energy of the system
  • Inelastic collisions convert kinetic energy to internal energy or vice versa through excitation, de-excitation, ionization, and recombination processes
• Radiative energy transfer involves emission and absorption of photons
  • Emission occurs when excited particles release energy as photons through line emission, bremsstrahlung, and recombination radiation
  • Absorption happens when particles absorb photons, increasing their internal energy via photoionization and photoexcitation
• Energy balance in plasmas is reached when energy gain and loss mechanisms are balanced, with collisional and radiative processes contributing to the overall balance

Thermodynamics of plasma equilibrium

• First law of thermodynamics (energy conservation) states that change in internal energy equals heat added plus work done and applies to plasma systems considering collisional and radiative energy transfer
• Second law of thermodynamics (entropy and irreversibility) indicates that isolated systems tend towards maximum entropy and thermal equilibrium, with plasma processes like collisions and radiation increasing entropy
• Plasma equilibrium includes:
  1. Thermal equilibrium: Uniform temperature throughout the plasma
  2. Chemical equilibrium: Balance between ionization and recombination processes
  3. Radiative equilibrium: Balance between emission and absorption of radiation
• Plasma stability analysis helps predict and control plasma behavior, as perturbations from equilibrium can lead to instabilities such as thermal, magnetic, and hydrodynamic instabilities