The statistically steady distributions P͑log E͒ and P e ͑log E e ͒ of waveform field E and envelope field E e are studied for time-varying waves with stochastically driven amplitudes. The waves are represented in one dimension ͑1D͒ by a single mode or superposition of multiple independent modes, whose amplitudes follow stochastic differential equations. Both distributions at low fields follow power laws: P͑log E͒ ϰ E p and P e ͑log E e ͒ ϰ E e q with distinct exponents p and q. Transitions in both distributions are found between the single-mode and multimode cases, with the distributions in the latter essentially independent of the number N ͑provided N Ն 2͒ of modes. For N Ն 2, p Ϸ +1.0, q Ϸ +2.0, and both distributions agree quantitatively with independent analytic predictions. Applications to Langmuir waves observed in Earth's polar cusp ionosphere show that both distributions for N Ն 2 agree quantitatively with the respective observations, suggesting that the Langmuir waves may be 1D and have a stochastic driver.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.