Beta and Operating Limits

Beta measures plasma pressure against magnetic pressure; the burner operates within a band where the plasma stays MHD-stable.

Pressure versus field

Beta is the ratio of plasma pressure to magnetic pressure. High beta is desirable — more fusion power for a given field — but too high a beta drives magnetohydrodynamic (MHD) instabilities that break confinement. Every magnetic confinement machine operates below a beta limit, and the burner is no exception. Its operating band is chosen to stay comfortably stable.

Mirrors and beta

Open systems like mirrors can in principle run at relatively high beta, but they must be shaped to remain MHD-stable — see minimum-B stability. The magnetic geometry is arranged so that the plasma sits in a region where increasing pressure does not trigger interchange or ballooning modes. Staying within the resulting band is a hard operating constraint the control system enforces.

# beta as pressure ratio (illustrative)
mu0 = 4e-7 * 3.14159265
def beta(n, T_keV, B):
    p = n * (T_keV*1e3*1.602e-19)   # pressure, Pa (single species, illustrative)
    p_mag = B*B/(2*mu0)
    return p/p_mag
print(round(beta(2.5e20, 90, 3.0),4))  # central-cell-like inputs

What sets the limits

• MHD stability caps the achievable beta — see minimum-B
• Microinstabilities can enhance transport below the MHD limit
• Radiation losses set a lower bound on useful temperature
• Component heat limits bound density and power

The numbers in the code are illustrative inputs, not the frozen design point; the load-bearing canon is the field set (26.49 T plug, 17 T throat) and the 5.44% neutron fraction. Beta and its limits are computed in the design study and are part of what the test unit must confirm — no net-gain claim precedes that.

Operating a comfortable distance below the stability limit, rather than pressing right against it, is a deliberate choice for a machine meant to run continuously and reliably — robustness is worth more than the last increment of plasma pressure for a generator serving a firm load.