{'fraction_non_alphanumeric': 0.018609742747673783, 'fraction_numerical': 0.0, 'mean_word_length': 5.459363957597173, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Intrinsic stochasticity in fusion plasmas

In magnetically confined fusion plasmas, the stability and confinement of the plasma edge region place important constraints on the capability to reach and sustain the high temperatures and power levels needed for fusion burning. Edge instabilities have the potential to be dangerously large and their control is critical for future burning plasmas. Recent results suggest that the importance of intrinsic stochasticity, beyond the effects of small-scale background plasma fluctuations, on macroscopic stability and confinement near the plasma edge. Two main sources exist. The toroidal magnetic field behaves like a Hamiltonian system with two degrees of freedom. A favorable configuration for confinement has a D-shaped cross-section, with magnetic X-points at one or both corners of the D. Small non-axisymmetric disturbances of the plasma boundary surface lead to the development of a homoclinic-type magnetic tangle around the X-point(s) that distorts the magnetic boundary and produces a stochastic field over the edge region. The D-shape also sustains a steep pressure gradient near the plasma edge. Plasma instabilities driven by the gradient have a broad spectrum of moderate to high toroidal harmonics; their nonlinear interaction contributes to the stochasticity. Large scale magnetohydrodynamic (MHD) numerical simulations allow the plasma boundary to move freely inside a surrounding, near-vacuum region of unconfined field lines. They show that MHD edge instabilities can self-consistently generate a stochastic magnetic tangle. The tangle evolves with the instability to reproduce important features of experimental observations. The results suggest that the plasma edge always has a non-negligible degree of stochasticity that affects plasma stability and confinement.