Jump of the adiabatic invariant at a separatrix crossing: Degenerate cases

2012 ◽  
Vol 241 (5) ◽  
pp. 566-573 ◽  
Author(s):  
Alexei Vasiliev ◽  
Anatoly Neishtadt ◽  
Anton Artemyev ◽  
Lev Zelenyi
Keyword(s):  
Adiabatic Invariant ◽  
Separatrix Crossing ◽  
Degenerate Cases

scholarly journals Stochastic Diffusion of Energetic Ions in Wendelstein-Type Stellarators

2018 ◽  
Vol 63 (6) ◽  
pp. 495
Author(s):  
A. V. Tykhyy
Keyword(s):  
Diffusion Coefficient ◽  
Adiabatic Invariant ◽  
Stochastic Diffusion ◽  
Energetic Ions ◽  
Separatrix Crossing

The collisionless stochastic diffusion of energetic ions in optimized stellarators of the Wendelstein type has been considered. The phenomenon concerned was predicted earlier in the framework of a simplified theory describing the separatrix crossing by ions. The jumps of the adiabatic invariant in magnetic configurations of a stellarator are calculated. The analysis of the results obtained confirms the importance of the stochastic diffusion and demonstrates that the diffusion coefficient can considerably exceed the available result.

Adiabatic-invariant change due to separatrix crossing

1986 ◽  
Vol 34 (5) ◽  
pp. 4256-4275 ◽  
Author(s):  
John R. Cary ◽  
D. F. Escande ◽  
J. L. Tennyson
Keyword(s):  
Adiabatic Invariant ◽  
Separatrix Crossing

Change of the Adiabatic Invariant due to Separatrix Crossing

1986 ◽  
Vol 56 (20) ◽  
pp. 2117-2120 ◽  
Author(s):  
J. L. Tennyson ◽  
John R. Cary ◽  
D. F. Escande
Keyword(s):  
Adiabatic Invariant ◽  
Separatrix Crossing

scholarly journals Some Remarks on the Regular Splitting of Quasi-Polynomials with Two Delays. Characterization of Double Roots in Degenerate Cases

2020 ◽  
Vol 53 (2) ◽  
pp. 4386-4391
Author(s):  
Alejandro Martínez-González ◽  
César-Fernando Méndez-Barrios ◽  
Silviu-Iulian Niculescu
Keyword(s):  
Regular Splitting ◽  
Two Delays ◽  
Degenerate Cases

Separatrix crossing and large scale diffusion in low-frequency three-wave systems

1998 ◽  
Vol 58 (3) ◽  
pp. 3768-3776 ◽  
Author(s):  
B. Weyssow ◽  
J. D. Reuss ◽  
J. Misguich
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Separatrix Crossing

scholarly journals Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

2014 ◽  
Vol 119 (9) ◽  
pp. 7615-7635 ◽  
Author(s):  
Liheng Zheng ◽  
Anthony A. Chan ◽  
Jay M. Albert ◽  
Scot R. Elkington ◽  
Josef Koller ◽  
...  
Keyword(s):  
Stochastic Modeling ◽  
Three Dimensional ◽  
Radiation Belts ◽  
Adiabatic Invariant

scholarly journals Ion motion in the current sheet with sheared magnetic field – Part 1: Quasi-adiabatic theory

2013 ◽  
Vol 20 (1) ◽  
pp. 163-178 ◽  
Author(s):  
A. V. Artemyev ◽  
A. I. Neishtadt ◽  
L. M. Zelenyi
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Analytical Description ◽  
Particle Energy ◽  
Tangential Component ◽  
Adiabatic Invariant ◽  
Ion Motion ◽  
Adiabatic Theory ◽  
Fast Oscillations ◽  
The Magnetic Field

Abstract. We present a theory of trapped ion motion in the magnetotail current sheet with a constant dawn–dusk component of the magnetic field. Particle trajectories are described analytically using the quasi-adiabatic invariant corresponding to averaging of fast oscillations around the tangential component of the magnetic field. We consider particle dynamics in the quasi-adiabatic approximation and demonstrate that the principal role is played by large (so called geometrical) jumps of the quasi-adiabatic invariant. These jumps appear due to the current sheet asymmetry related to the presence of the dawn–dusk magnetic field. The analytical description is compared with results of numerical integration. We show that there are four possible regimes of particle motion. Each regime is characterized by certain ranges of values of the dawn–dusk magnetic field and particle energy. We find the critical value of the dawn–dusk magnetic field, where jumps of the quasi-adiabatic invariant vanish.

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