Nonresonant CR-current instability — mode solver & field animation

Solves h₁(ω)=0 (electrostatic) and h₂(ω)² = h₃(ω)² (transverse, R/L) from Gupta, Caprioli & Haggerty Eqs. (A9)–(A11), then animates the resulting perturbed electron/ion velocities and E₁, B₁, J₁ fields along x̂.

x ■ y ■ z ■

drag = orbit · scroll = zoom · right-drag = pan

Plasma / CR parameters

CR charge sign

(m_e = 1)

electron bulk speed / c

Transverse branch

Initial field amplitudes

electrostatic

, — B_z1 is the phase-0 reference (paper's Eq. 14 convention). comes out of the eigenvector of the solved matrix, not from a slider. are then rebuilt from via , (Eq. A5).

Show

electron velocity v₁ₑ ion (proton) velocity v₁ᵢ E₁ₓ arrows (electrostatic) J₁ₓ arrows

Visual scale & playback

v scale

B scale

E scale

J scale

speed

curve thickness

growth cap (envelope ×)

electron v ion v B₁ E₁ J₁

Formulas transcribed directly from the uploaded equations (A1)–(A11), Gupta, Caprioli & Haggerty. Units: c=1, Ω_ci=1, e=1, m_e=1, so ω_pi=1/v_A0, ω_ce=m_i/m_e=m_i. Complex ω is found numerically (Newton–Raphson, multi-seed) — double-check against the paper before citing growth rates.