Linear Pinch Equilibrium of Non-Neutral Plasma Revisited: Phenomenological Consequences of a Numerical Accuracy Problem

F. L. Braga, D. N. Soares

Abstract


Weibel in 1959 under considerations of a collisionless non-neutral cylindrical plasma column studied a linear pinch confinement equilibrium. As reported here, due to non-linearity of the ordinary differential equations obtained for the electrostatic and magnetostatic fields is possible to demonstrate that the confining features previously obtained are extremely dependent on the initial conditions, and the arrangement of two parameters (β - the ratio between ion and electron mass; M/KT - ratio between relativistic rest energy associated with the pair electron-ion and thermal energy kT ) related to the plasma column characteristics. We investigated in this paper the plasma column behavior (confining or non-confining) under modifications of that set of parameters. We detected a set of parameters values that imposes a confining configuration with an electronic skin effect on the plasma column, not yet reported or discussed in the literature.


Keywords


Locally Non-neutral Plasma; Linear Pinch; Skin Effect; Numerical Accuracy

References


P. Helander. Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys., 77(8):087001, 2014. doi:10.1088/0034-4885/77/8/087001.

M. D. Kruskal and R. M. Kulsrud. Equilibrium of a Magnetically Confined Plasma in a Toroid. Phys. Fluids, 1(4):265–274, 1958. doi:10.1063/1.1705884.

D. Mascali, G. Torrisi, L. Neri, G. Sorbello, G. Castro, L. Celona, and S. Gammino. 3D-full wave and kinetics numerical modelling of electron cyclotron resonance ion sources plasma: steps towards self-consistency. Eur. Phys. J. D, 69(1), 2015. doi:10.1140/epjd/e2014-50168-5.

C. B. Smiet, S. Candelaresi, A. Thompson, J. Swearngin, J. W. Dalhuisen, and D. Bouwmeester. Self-Organizing Knotted Magnetic Structures in Plasma. Phys. Rev. Lett., 115:095001, Aug 2015. doi:10.1103/PhysRevLett.115.095001.

W. A. Newcomb. Hydromagnetic stability of a diffuse linear pinch. Ann. Phys., 10(2):232–267, 1960. doi:10.1016/0003-4916(60)90023-3.

J. Koliner, M. Cianciosa, J. Boguski, J. Anderson, J. Hanson, B. Chapman, D. Brower, D. Den Hartog, W. Ding, J. Duff, et al. Three dimensional equilibrium solutions for a current-carrying reversed-field pinch plasma with a close-fitting conducting shell. Physics of Plasmas, 23(3):032508, 2016.

U. Shumlak, B. Nelson, E. Claveau, E. Forbes, R. Golingo, M. Hughes, R. Oberto, M. Ross, and T. Weber. Increasing plasma parameters using sheared flow stabilization of a z-pinch. Physics of Plasmas, 24(5):055702, 2017.

E. Kroupp, E. Stambulchik, A. Starobinets, D. Osin, V. Fisher, D. Alumot, Y. Maron, S. Davidovits, N. Fisch, and A. Fruchtman. Turbulent stagnation in a z-pinch plasma. Physical Review E, 97(1):013202, 2018.

J. Goedbloed. Stabilization of magnetohydrodynamic instabilities by force-free magnetic fields. Physica, 53(4):501–534, 1971. doi:10.1016/0031-8914(71)90113-3.

E. S. Weibel. On the Confinement of a Plasma by Magnetostatic Fields. Phys.Fluids, 2(1):52–56, 1959. doi:10.1063/1.1724391.

F. F. Chen and M. D. Smith. Plasma. John Wiley and Sons, Inc., 2005. doi:10.1002/0471743984.vse9673.

G. Schmidt and D. Finkelstein. Magnetically Confined Plasma with a Maxwellian Core. Phys. Rev., 126:1611–1615, Jun 1962. doi:10.1103/PhysRev.126.1611.

C. C. Pian and A. W. McClaine. Techniques for the solution of MHD generator flows. Comput. Fluids, 12(4):319–338, 1984. doi:10.1016/0045-7930(84)90013-6.

P. Gratreau and P. Giupponi. Vlasov equilibria of cylindrical relativistic electron beams of arbitrary high intensity. Phys. Fluids, 20(3):487–493, 1977. doi:10.1063/1.861887.

B. M. Annaratone, W. Jacob, C. Arnas, and G. E. Morfill. Critical review of complex plasma (dusty plasma) diagnostics and manipulation techniques for the fusion community and others. IEEE Transactions on Plasma Science, 37(1):270–280, Jan 2009. doi:10.1109/TPS.2008.2006269.

P. K. Shukla and A. A. Mamun. Introduction to dusty plasma physics. Plasma Physics and Controlled Fusion, 44(3):395, 2002. doi:10.1088/0741-3335/44/3/701.

A. A. Fridman, L. Boufendi, T. Hbid, B. V. Potapkin, and A. Bouchoule. Dusty plasma formation: Physics and critical phenomena. theoretical approach. Journal of Applied Physics, 79(3):1303–1314, 1996. doi:10.1063/1.361026.

S. Mayout, L. A. Gougam, and M. Tribeche. Effects of ionization and ion loss on dust ion-acoustic solitary waves in a collisional dusty plasma with suprathermal electrons. Physics of Plasmas, 23(3):033701, 2016. doi:10.1063/1.4942935.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA, 3 edition, 2007.

D. Griffiths. Introduction to Electrodynamics. Prentice Hall, 1999.

D. Forcella, J. Zaanen, D. Valentinis, and D. Van Der Marel. Electromagnetic properties of viscous charged fluids. Physical Review B, 90(3):035143, 2014.

F. Halpern, P. Ricci, S. Jolliet, J. Loizu, J. Morales, A. Mosetto, F. Musil, F. Riva, T.-M. Tran, and C. Wersal. The gbs code for tokamak scrape-off layer simulations. Journal of Computational Physics, 315:388–408, 2016.


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