Space Plasma Quick Calculator
Shared inputs below are used by all calculators. Units: \(n_i\) in cm⁻³, \(B\) in nT, \(v_\perp\) in km/s, \(T_i\) in K, custom mass in amu.
Shared Inputs
MHD Speeds: \(V_A\) & \(C_s\)
Alfvén speed \(V_A\):
— km/s
Ion sound speed \(C_s\):
— km/s
Formulas: \(V_A=\dfrac{B}{\sqrt{\mu_0 \rho}}\), \(\rho=m_i n_i\); \(C_s=\sqrt{\gamma k_B T_i/m_i}\) (ion-only).
Plasma β and Ion Thermal Speed
Assuming \(T_i=T_e\), Plasma β :
\[
\beta \;=\; \frac{2\,\mu_0\,(p_i+p_e)}{B^2}
\;=\; \frac{2\,\mu_0\,n_i k_B (T_i+T_e)}{B^2}
\]
—
Ion thermal speed \(v_{th,i}=\sqrt{2kT_i/m_i} \;\approx\; C_s\):
— km/s
Ion Inertial Length \(d_i\)
\(d_i\) (assumes \(q=e\)):
— km
Formula: \(d_i=\sqrt{m_i/(\mu_0 e^2 n_i)}\) (singly charged assumption).
Ion Gyroradius \(r_g\)
\(r_g\) (assumes \(v_\perp = v\)):
— km
Formula: \(r_g = \dfrac{m_i v_\perp}{Z e B}\).
Gyrofrequency \(\Omega_i\) & \(\Omega_e\); with lower hybrid frequency \(= \sqrt{\Omega_i \Omega_e}\)
Ion gyrofrequency \(\Omega_i\) (rad/s):
—
Ion gyrofrequency \(f_i\) (Hz):
—
Ion gyro Period \(T_{gi}\) (s):
—