{'fraction_non_alphanumeric': 0.0446927374301676, 'fraction_numerical': 0.00186219739292365, 'mean_word_length': 5.142857142857143, '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}}
Gyrokinetic equations for strong-gradient regions

A gyrokinetic theory is developed under a set of orderings applicable to the edge region of tokamaks and other magnetic confinement devices, as well as to internal transport barriers. The result is a practical set equations that is valid for large perturbation amplitudes [qδψ/T=O(1), where δψ=δφ-ν∥δA∥/c], which is straightforward to implement numerically, and which has straightforward expressions for its conservation properties. Here, δφ and δA∥ are the perturbed electrostatic and parallel magnetic potentials, ν∥ is the particle velocity, c is the speed of light, and T is the temperature. The derivation is based on the quantity ɛ≡(ρ/λ⊥)qδψ/T≪1 as the small expansion parameter, where ρ is the gyroradius and λ⊥ is the perpendicular wavelength. Physically, this ordering requires that the E×B velocity and the component of the parallel velocity perpendicular to the equilibrium magnetic field are small compared to the thermal velocity. For nonlinear fluctuations saturated at “mixing-length” levels (i.e., at a l...