Plasma Pressure Calculator

Plasma pressure is the total kinetic (thermal) pressure exerted by all charged particle species in a plasma, arising from their random thermal motion, exactly like the pressure of an ordinary ideal gas. Since a plasma contains both electrons and ions, its total pressure is the sum of the pressure each species contributes on its own.

p = neTee + niTie, where ne and ni are the electron and ion number densities, Te and Ti are their respective temperatures in electronvolts, and e is the elementary charge (which converts the eV-density product into pascals). Each term is simply that species' own ideal-gas pressure, nTe.

In many real plasmas, especially those heated rapidly or with relatively low collision rates, energy exchange between electrons and ions is slow enough that the two species settle into different temperatures. This calculator handles that general case directly, rather than assuming Te = Ti as some simplified formulas do.

Heating mechanisms often couple more directly to one species (for example, ohmic heating and electron-cyclotron heating primarily heat electrons, while neutral beam injection primarily heats ions), and the electron-ion collisional energy exchange time can be much longer than the heating or confinement timescale, letting a temperature difference persist.

Plasma beta is exactly the ratio of this total plasma pressure to the magnetic pressure, β = p/(B²/2μ₀). This calculator computes the numerator (or its Te=Ti special case) that the <a href="/science/plasma-physics/plasma-beta-parameter-calculator/">Plasma Beta Parameter Calculator</a> compares against the magnetic pressure.

Plasmas are quasi-neutral overall, so for a plasma with only singly-charged ions (Z=1), electron density must equal ion density (ne=ni) to keep the total charge density near zero. For multiply-charged ions (charge state Z), quasi-neutrality instead requires ne = Z·ni.

Yes, exactly, each species obeys the same p = nkT (or p = nTe in electronvolt units) relationship as an ordinary ideal gas, since the derivation from kinetic theory does not depend on whether the particles are neutral molecules or charged plasma particles. The only difference for a plasma is that there are typically two or more species contributing pressure simultaneously.

No, this calculator computes only the kinetic (thermal) pressure from particle motion. Magnetic pressure, B²/2μ₀, is a separate quantity computed by the <a href="/science/plasma-physics/plasma-beta-parameter-calculator/">Plasma Beta Parameter Calculator</a>, which compares the two.

A magnetically confined plasma's thermal pressure must be balanced by the confining magnetic pressure, or the plasma will expand and lose confinement. Higher achievable pressure at a given magnetic field (higher plasma beta) directly translates into more fusion power for the same, expensive superconducting magnet system.

A tokamak achieves comparable or higher pressure than the solar corona despite the corona having a vastly larger volume, because the tokamak's density and temperature are both far higher, illustrating just how extreme laboratory fusion conditions are compared to a natural stellar atmosphere.