The Debye Debrief

Basics

100

The curl of B = μ₀ * j + u₀ * ε₀ ∂E/∂t

What is Ampere-Maxwell's law?

200

m * dv/dt = q ( E + v x B)

What is the equation of motion for charged particles in fields?

300

The square root of 1 / ( 1 - v² / c² )

What is the Lorentz Factor?

400

The square root of (ε₀ * k * T) / ( n₀ * e²)

What is the Debye Length?

500

1 / μ₀ * (E x B)

What is the Poynting Flux?

Linear Waves

100

ω² = ω_p² + k² * c²

What is the dispersion relation?

200

The square root of ( n_e * e² ) / ( ε₀ * m_e )

What is the electron plasma frequency?

300

( m_e * ω² ) / ( 4π * e²)

What is the critical density?

400

The square root of k * T_e / m_i

What is the ion sound speed?

500

-(π / 8)^1/2 * ω_pe² / ( k³ * λ_De³ ) * exp[ - ( 1 + 3 * k² * λ²_De ) / ( 2 * k² * λ²_De ) ]

What is the Landau damping rate?

MHD

100

d/dt = ∂/∂t + v * ∇_r

What is the continuity equation?

200

d/dt ( p * n^-γ ) = 0 where γ=( μ + 2 ) / μ and μ is the # of dimensions

What is the evolution of plasma pressure?

300

ω_p / 2 , or the maximum of | k * v₀ | where v_e=v₀+δv

$$$DAILY DOUBLE$$$ What is the maximum growth rate for very long perturbations of counter-streaming electrons?

400

Type of surface: dΨ(t)/dt = ∫_∂S(t) (v-u)(t) x B(t) * dl

What are frozen surfaces?

500

Magnetic field transport eq: ∂B/∂t - ∇ x (u x B) - η / μ₀ * ∇²B = 0

What is resistive diffusion of magnetic field lines?

Collisions

100

Both the quantities L² / 𝜏 and ( q₁ * q₂ ) / ( 4 * π * ε₀ * μ * v₀² )

What are the Diffusion coefficient and the b₉₀ parameter?

200

dσ/dΩ = b₉₀² / [ 4 * sin⁴( θ / 2 ) ]

What is the Rutherford cross section?

300

λ_D / b₉₀ or equivalently [ ( ε₀ * T_e ) / ( e² * n_e ) ]^1/2 * ( 4 * π * ε₀ * μ * v₀² ) / (q₁ * q₂ )

What is the Coulomb logarithm?

400

𝜈_p * ( 2 * m₁ ) / ( m₁ + m₂ ) where 𝜈_p = σ_p * n_t * v₀ , σ_p the effective momentum cross section and n_t the particles per unit of volume moving at speed v₀

What is the energy loss frequency (𝜈_k)?

500

1.65 * 10^-9 * ln(Λ) / ( T_e^3/2 [keV] ) [Ωm]

What is the Spitzer resistivity?

Tokamak Physics

100

Both the quantities |q| * B / m and v_⟂ / Ω

What are the cyclotron frequency and the Larmor radius?

200

( F x B ) / ( q * B² ) or just ( E x B ) / B² if only Electric field present

What is the E x B drift of the gyrocenter?

300

( m * v_⟂² * B x ∇B ) / ( q * 2B * B²)

What is Grad B drift?

400

( m * v_∥² * R_c x B ) / ( q * B² * R_c² )

What is curvature drift?

500

Type of motion: F_∥=-μ * ∇_∥ * B with constant μ where μ=m * v_⟂² / ( 2 * B ) is the magnetic moment

What is mirror motion?