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Neoclassical transport: Difference between revisions
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* A fixed geometry. Neoclassical transport is calculated in a static magnetic geometry. In actual experiments (especially Tokamaks), the magnetic field evolves along with the plasma itself, leading to a modification of net transport. While a slow evolution (with respect to typical transport time scales) should not be problematic, rapid changes (such as magnetic reconnections) are outside of the scope of the theory. | * A fixed geometry. Neoclassical transport is calculated in a static magnetic geometry. In actual experiments (especially Tokamaks), the magnetic field evolves along with the plasma itself, leading to a modification of net transport. While a slow evolution (with respect to typical transport time scales) should not be problematic, rapid changes (such as magnetic reconnections) are outside of the scope of the theory. | ||
* The remoteness of system boundaries. Particle orbits in complex geometries can be rather wide, in some circumstances, so that the presence of system boundaries is "felt" by the plasma. Presumably, and since Neoclassical Theory assumes that the system is essentially infinite, this explains why Neoclassical Theory tends to fail near the edge of the plasma. Internal Transport Barriers may also produce non-Neoclassical effects. | * The remoteness of system boundaries. Particle orbits in complex geometries can be rather wide, in some circumstances, so that the presence of system boundaries is "felt" by the plasma. Presumably, and since Neoclassical Theory assumes that the system is essentially infinite, this explains why Neoclassical Theory tends to fail near the edge of the plasma. Internal Transport Barriers may also produce non-Neoclassical effects. | ||
* The linearity of the model. Neoclassical theory is a linear theory in which profiles are computed from sources, boundary conditions, and transport coefficients (that depend linearly on the profiles). No non-linear feedback of the profiles on the transport coefficients is contemplated. However, there are many | * The linearity of the model. Neoclassical theory is a linear theory in which profiles are computed from sources, boundary conditions, and transport coefficients (that depend linearly on the profiles). No non-linear feedback of the profiles on the transport coefficients is contemplated. However, there are many experimental studies that show that the profiles feed back non-linearly on transport (via [[Turbulence|turbulence]]), leading to some degree of [[Self-Organised Criticality|self-organisation]]. | ||
* Locality. Neoclassical theory is a theory of diffusion, and therefore it assumes that particle motion between collisions is small with respect to any other relevant spatial scales. This assumption then allows writing down differential equations, expressing the fluxes in terms of ''local'' gradients. It cannot be discarded that this basic assumption is violated under specific conditions, which may include the low-collisionality limit, and particles transported in ''streamers''. Typically, this would then give rise to [[Non-diffusive transport|super-diffusion]]. | * Locality. Neoclassical theory is a theory of diffusion, and therefore it assumes that particle motion between collisions is small with respect to any other relevant spatial scales. This assumption then allows writing down differential equations, expressing the fluxes in terms of ''local'' gradients. It cannot be discarded that this basic assumption is violated under specific conditions, which may include the low-collisionality limit, and particles transported in ''streamers''. Typically, this would then give rise to [[Non-diffusive transport|super-diffusion]]. | ||
* Markovianity. A second assumption underlying diffusive models (including Neoclassics) is Markovianity, implying that the motion of any particle is only determined by its current velocity and position. However, there are situations, such as stochastic magnetic field regions, persistent turbulent eddies, or transport barriers, where this assumption may be violated (due to trapping effects, so that the preceding history of the particle trajectory becomes important). Typically, this would then give rise to [[Non-diffusive transport|sub-diffusion]]. | * Markovianity. A second assumption underlying diffusive models (including Neoclassics) is Markovianity, implying that the motion of any particle is only determined by its current velocity and position. However, there are situations, such as stochastic magnetic field regions, persistent turbulent eddies, or transport barriers, where this assumption may be violated (due to trapping effects, so that the preceding history of the particle trajectory becomes important). Typically, this would then give rise to [[Non-diffusive transport|sub-diffusion]]. | ||