Classical diffusion is a key concept in fusion power and other fields where a plasma is confined by a magnetic field. It considers collisions between ions in the plasma that cause the particles to move to different paths and eventually leave the confinement volume. It scales with 1/B2, where B is the magnetic field strength, implies that confinement times can be greatly improved with small increases in field strength. In practice, the rates suggested by classical diffusion have not been found in real-world machines.
Description
is a random walk process that can be quantified by the two key parameters: Δx, the step size, and Δt, the time interval when the walker takes a step. Thus, the diffusion coefficient is defined as D≡2/. When an ion is placed in a magnetic field, it will orbit the field lines while continuing to move along that line with whatever initial velocity it had. This produces a helical path through space. Since the axial velocities will have a range of values, often based on the Maxwell-Boltzmann statistics, this means the particles in the plasma will pass by others as they overtake them or are overtaken. If one considers two such ions travelling along parallel axial paths, they can collide whenever their orbits intersect. In most geometries, this means there is a significant difference in the instantaneous velocities when the collide - one might be going "up" while the other would be going "down" in their helical paths. This causes the collisions to scatter the particles, making them random walks. Eventually, this process will cause any given ion to eventually leave the boundary of the field, and thereby escape "confinement". In a uniform magnetic field, a particle undergoes random walk across the field lines by the step size of gyroradius ρ≡vth/Ω, where vth denotes the thermal velocity, and Ω≡qB/m, the gyrofrequency. The steps are randomized by the collisions to lose the coherence. Thus, the time step, or the decoherence time, is inverse of the collisional frequency νc. The rate of diffusion is given by νcρ2, with the rather favorable B−2 scaling law.
In practice
When the topic of controlled fusion was first being studied, it was believed that the plasmas would follow the classical diffusion rate, and this suggested that useful confinement times would be relatively easy to achieve. However, in 1949 a teamstudying plasma arcs as a method of isotope separation found that the diffusion time was much greater than what was predicted by the classical method. David Bohm suggested it scaled with B. If this is true, Bohm diffusion would mean that useful confinement times would require impossibly large fields. In practice, machines have demonstrated a wide array of diffusion rates between these two extremes.
