Tokamak Bootstrap Current Fraction Calculator
Neoclassical Magnetohydrodynamics: Calculate self-generated neoclassical bootstrap current ($I_{bs}$), bootstrap fraction ($f_{bs}$), and non-inductive steady-state sustainment.
Tokamak Equilibrium & Beta Parameters
Bootstrap Current & Auxiliary Drive Output
Neoclassical Bootstrap Current & Steady-State Fusion
The bootstrap current represents one of the most remarkable self-organization phenomena in high-temperature magnetized plasmas, providing a natural non-inductive current sustainment mechanism.
1. Scaling Relationships
ε = a / R₀ [Inverse Aspect Ratio] f_t ≈ 1.46·√ε - 0.46·ε [Trapped Particle Fraction] f_bs ≈ C_bs · √ε · β_p [Bootstrap Fraction] I_bs = f_bs · I_p [Self-Driven Current]
2. Advanced Tokamak (AT) Strategy
By driving $\beta_p > 2.0$, modern steady-state pilot plant designs target $f_{bs} > 0.80$, requiring only a minor seed current driven centrally by Electron Cyclotron Current Drive (ECCD) to maintain MHD stability.
Frequently Asked Questions
What is the neoclassical bootstrap current in a tokamak?
The bootstrap current is an internally generated, steady-state toroidal electric current that arises spontaneously from the radial pressure gradient (\nabla p) and neoclassical banana orbits of trapped particles. Predicted theoretically by R.J. Bickerton, J.W. Connor, and J.B. Taylor in 1971 and verified experimentally on TFTR in 1986, it reduces or eliminates the need for external inductive transformer drive or RF current drive power.
Why is bootstrap current essential for steady-state fusion reactors?
Tokamaks are intrinsically pulsed devices because the central solenoid transformer will saturate when its magnetic flux limit is reached. To operate continuously (steady-state power plant like DEMO or commercial reactors), 100% of the toroidal plasma current must be driven non-inductively. Since auxiliary RF/NBI current drive efficiency is low (requiring hundreds of megawatts of recirculating electric power), a high bootstrap fraction (f_bs >= 75%) is critical to economic viability.
How can the bootstrap current fraction be maximized?
The bootstrap fraction scales as $f_{bs} \propto \sqrt{a/R_0} \cdot \beta_p$. To maximize $f_{bs}$, fusion physicists engineer Advanced Tokamak (AT) scenarios with low aspect ratio (spherical tokamaks or compact designs), high poloidal beta $\beta_p$, reversed or flat central magnetic shear, and steep internal transport barriers (ITBs) that create sharp localized pressure gradients.