Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-24T02:03:24.742Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral analysis of forced turbulence in a non-neutral plasma

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  21 June 2017

S. Chen ,
G. Maero  and
M. Romé
S. Chen
Affiliation:
Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, Sichuan 621900, PR China
G. Maero
Affiliation:
Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy INFN Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
M. Romé*
Affiliation:
Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy INFN Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

Keywords

magnetized plasmasplasma dynamicsplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 3 , June 2017 , 705830303
Copyright
© Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amoretti, M., Durkin, D., Fajans, J., Pozzoli, R. & Romé, M. 2001 Asymmetric vortex merger: experiments and simulations. Phys. Plasmas 8, 3865–3868.CrossRefGoogle Scholar
Antoni, V., Carbone, V., Martines, E., Regnoli, G., Serianni, G., Vianello, N. & Veltri, P. 2001 Electrostatic turbulence intermittency and MHD relaxation phenomena in a RFP plasma. Europhys. Lett. 54, 51–57.CrossRefGoogle Scholar
Baroud, C. N., Plapp, B. B., She, Z. S. & Swinney, H. L. 2002 Anomalous self-similarity in a turbulent rapidly rotating fluid. Phys. Rev. Lett. 88, 114501.CrossRefGoogle Scholar
Bettega, G., Cavaliere, F., Cavenago, M., Illiberi, A., Pozzoli, R. & Romé, M. 2007a Experimental and numerical analysis of the electron injection in a Malmberg–Penning trap. Phys. Plasmas 14, 042104.CrossRefGoogle Scholar
Bettega, G., Cavaliere, F., Paroli, B., Cavenago, M., Pozzoli, R. & Romé, M. 2007b Excitation of the $l=2$ azimuthal mode in a pure electron plasma. Phys. Plasmas 14, 102103.CrossRefGoogle Scholar
Bettega, G., Cavaliere, F., Paroli, B., Pozzoli, R., Romé, M. & Cavenago, M. 2008 Excitation of the $l=2$ diocotron mode with a resistive load. Phys. Plasmas 15, 032102.CrossRefGoogle Scholar
Bettega, G., Paroli, B., Pozzoli, R. & Romé, M. 2009a Excitation of the $l=3$ diocotron mode in a pure electron plasma by means of a rotating electric field. J. Appl. Phys. 105, 053303.CrossRefGoogle Scholar
Bettega, G., Pozzoli, R. & Romé, M. 2009b Multiresolution analysis of the two-dimensional free decaying turbulence in a pure electron plasma. New J. Phys. 11, 053006.CrossRefGoogle Scholar
Carbone, V., Regnoli, G., Martines, E. & Antoni, V. 2000 Intermittency and self-similarity in plasma edge fluctuations. Phys. Plasmas 7, 445–447.CrossRefGoogle Scholar
Chen, S., Maero, G. & Romé, M. 2015 Effect of initial conditions on electron-plasma turbulence: a multiresolution analysis. J. Plasma Phys. 81, 495810511.CrossRefGoogle Scholar
Chernyshov, A. A., Karelsy, K. V. & Petrosyan, A. S. 2010 Forced turbulence in large-eddy simulation of compressible magnetohydrodynamic turbulence. Phys. Plasmas 17, 102307.CrossRefGoogle Scholar
Danielson, J. R., Dubin, D. H. E., Greaves, R. G. & Surko, C. M. 2015 Plasma and trap-based techniques for science with positrons. Rev. Mod. Phys. 87, 247–306.CrossRefGoogle Scholar
Danielson, J. R., Weber, T. R. & Surko, C. M. 2006 Plasma manipulation techniques for positron storage in a multicell trap. Phys. Plasmas 13, 123502.CrossRefGoogle Scholar
Davidson, R. C. 1990 An Introduction to the Physics of Nonneutral Plasmas. Addison-Wesley.Google Scholar
DiSciacca, J., Marshall, M., Marable, K., Gabrielse, G., Ettenauer, S., Tardiff, E., Kalra, R., Fitzakerley, D. W., George, M. C., Hessels, E. A. et al. 2013 One-particle measurement of the antiproton magnetic moment. Phys. Rev. Lett. 110, 130801.CrossRefGoogle ScholarPubMed
Driscoll, C. F. & Fine, K. S. 1990 Experiments on vortex dynamics in pure electron plasmas. Phys. Fluids B 2, 1359–1366.CrossRefGoogle Scholar
Driscoll, C. F., Schecter, D. A., Jin, D. Z., Dubin, D. H. E., Fine, K. S. & Cass, A. C. 1999 Relaxation of 2D turbulence to vortex crystals. Phys. A 263, 284.Google Scholar
Dubin, D. H. E. & O’Neil, T. M. 1999 Trapped nonneutral plasmas, liquids and crystals (the thermal equilibrium states). Rev. Mod. Phys. 71, 87–172.CrossRefGoogle Scholar
Eggleston, D. L. & Carrillo, B. 2002 Amplitude scaling of asymmetry-induced transport in a non-neutral plasma trap. Phys. Plasmas 9, 786–790.CrossRefGoogle Scholar
Fajans, J., Backhaus, E. Y. & McCarthy, J. E. 1999a Equilibrium of highly asymmetric non-neutral plasmas. Phys. Plasmas 6, 12–18.CrossRefGoogle Scholar
Fajans, J., Gilson, E. & Friedland, L. 1999b Autoresonant (nonstationary) excitation of the diocotron mode in non-neutral plasmas. Phys. Rev. Lett. 82, 4444–4447.CrossRefGoogle Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–457.CrossRefGoogle Scholar
Farge, M., Schneider, K. & Kevlahan, N. 1999 Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis. Phys. Fluids 11 (8), 2187–2201.CrossRefGoogle Scholar
Fujiwara, M. C., Amoretti, M., Bonomi, G., Bouchta, A., Bowe, P. D., Carraro, C., Cesar, C. L., Charlton, M., Doser, M., Filippini, V. et al. 2004 Three-dimensional annihilation imaging of trapped antiprotons. Phys. Rev. Lett. 92, 065005.CrossRefGoogle ScholarPubMed
Gomberoff, K., Higaki, H., Ito, K. & Okamoto, H. 2016 Autoresonances of $m=2$ diocotron oscillations in non-neutral electron plasmas. Phys. Rev. E 94, 043204.Google ScholarPubMed
Gomberoff, K., Wurtele, J., Friedman, A., Grote, D. P. & Vay, J.-L. 2007 A method for obtaining three-dimensional computational equilibrium of non-neutral plasmas using WARP. J. Comput. Phys. 225, 1736–1752.CrossRefGoogle Scholar
Hollmann, E. M., Anderegg, F. & Driscoll, C. F. 2000 Confinement and manipulation of non-neutral plasmas using rotating wall electric fields. Phys. Plasmas 7, 2776–2789.CrossRefGoogle Scholar
Huang, X.-P., Anderegg, F., Hollmann, E. M., Driscoll, C. F. & O’Neil, T. M. 1997 Steady-state confinement of non-neutral plasmas by rotating electric fields. Phys. Rev. Lett. 78, 875–878.CrossRefGoogle Scholar
Hurst, N. C., Danielson, J. R., Dubin, D. H. E. & Surko, C. M. 2016 Evolution of a vortex in a strain flow. Phys. Rev. Lett. 117, 235001.CrossRefGoogle Scholar
Kabantsev, A. A. & Driscoll, C. F. 2015 TG wave autoresonant control of plasma temperature. AIP Conf. Proc. 1668, 020002.CrossRefGoogle Scholar
Kawai, Y., Kiwamoto, Y., Soga, Y. & Aoki, J. 2007 Propagation of axisymmetric Trivelpiece–Gould mode along vortex columns generated by diocotron instability. Phys. Plasmas 14, 102106.CrossRefGoogle Scholar
Kriesel, J. M. & Driscoll, C. F. 1998 Electron plasma profiles from a cathode with an $r^{2}$ potential variation. Phys. Plasmas 5, 1265–1272.CrossRefGoogle Scholar
Leith, C. E. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671–673.CrossRefGoogle Scholar
Lepreti, F., Romé, M., Maero, G., Paroli, B., Pozzoli, R. & Carbone, V. 2013 Scaling properties and intermittency of two-dimensional turbulence in pure electron plasmas. Phys. Rev. E 87, 063110.Google ScholarPubMed
Levy, R. H. 1965 Diocotron instability in a cylindrical geometry. Phys. Fluids 8, 1288–1295.CrossRefGoogle Scholar
Maero, G., Chen, S., Pozzoli, R. & Romé, M. 2015 Low-power radio-frequency excitation as a plasma source in a Penning–Malmberg trap: a systematic study. J. Plasma Phys. 81, 495810503.CrossRefGoogle Scholar
Maero, G., Paroli, B., Pozzoli, R. & Romé, M. 2011 Stabilizing effect of a nonresonant radio frequency drive on the $m=1$ diocotron instability. Phys. Plasmas 18, 032101.CrossRefGoogle Scholar
Maero, G., Paroli, B., Pozzoli, R. & Romé, M. 2016 Axial heating and temperature of RF-excited non-neutral plasmas in Penning–Malmberg traps. J. Instrum. 11, C09007.CrossRefGoogle Scholar
Maero, G., Romé, M., Lepreti, F. & Cavenago, M. 2014 Numerical study of a dust-contaminated electron plasma. Eur. Phys. J. D 68, 277.Google Scholar
Maggiore, M., Cavenago, M., Comunian, M., Chirulotto, F., Galatà, A., De Lazzari, M., Porcellato, A. M., Roncolato, C., Stark, S., Caruso, A. et al. 2014 Plasma-beam traps and radiofrequency quadrupole beam coolers. Rev. Sci. Instrum. 85, 02B909.CrossRefGoogle ScholarPubMed
Mallat, S. G. 1999 A Wavelet Tour of Signal Processing. Academic Press.Google Scholar
Malmberg, J. H. & deGrassie, J. S. 1975 Properties of nonneutral plasma. Phys. Rev. Lett. 35, 577–580.CrossRefGoogle Scholar
Matsumoto, M. & Nishimura, T. 1998 Mersenne twister: a 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. Model. Comput. Simul. 8, 3–30.CrossRefGoogle Scholar
Notte, J., Peurrung, A. J., Fajans, J., Chu, R. & Wurtele, J. S. 1992 Asymmetric stable equilibria of non-neutral plasmas. Phys. Rev. Lett. 69, 3056–3059.CrossRefGoogle ScholarPubMed
Onorato, M., Camussi, R. & Iuso, G. 2000 Small scale intermittency and bursting in a turbulent channel flow. Phys. Rev. E 61, 1447–1454.Google Scholar
Paroli, B., Bettega, G., Maero, G., Romé, M., Norgia, M., Pesatori, A. & Svelto, C. 2010a Electrostatic diagnostics of nanosecond pulsed electron beams in a Malmberg–Penning trap. Rev. Sci. Instrum. 81, 063503.CrossRefGoogle Scholar
Paroli, B., De Luca, F., Maero, G., Pozzoli, R. & Romé, M. 2010b Broadband radio frequency plasma generation in a Penning–Malmberg trap. Plasma Sources Sci. Technol. 19, 045013.CrossRefGoogle Scholar
Paroli, B., Maero, G., Pozzoli, R. & Romé, M. 2014 Diocotron modulation in an electron plasma through continuous radio-frequency excitation. Phys. Plasmas 21, 122102.CrossRefGoogle Scholar
Perrone, D., Nigro, G. & Veltri, P. 2011 A shell model turbulent dynamo. Astrophys. J. 735, 73.CrossRefGoogle Scholar
Peurrung, A. J. & Fajans, J. 1993a Experimental dynamics of an annulus of vorticity in a pure electron plasma. Phys. Fluids A 5, 493–499.CrossRefGoogle Scholar
Peurrung, A. J. & Fajans, J. 1993b A limitation to the analogy between pure electron plasmas and two-dimensional inviscid fluids. Phys. Fluids B 5, 4295–4298.CrossRefGoogle Scholar
Rauth, C., Ackermann, D., Blaum, K., Block, M., Chaudhuri, A., Di, Z., Eliseev, S., Ferrer, R., Habs, D., Herfurth, F. et al. 2008 First Penning trap mass measurement beyond the proton drip line. Phys. Rev. Lett. 100, 012501.CrossRefGoogle ScholarPubMed
Rivera, M., Vorobieff, P. & Ecke, R. E. 1998 Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys. Rev. Lett. 81, 1417–1420.CrossRefGoogle Scholar
Rodgers, D. J., Matthaeus, W. H., Mitchell, T. B. & Montgomery, D. C. 2010 Similarity decay of enstrophy in an electron fluid. Phys. Rev. Lett. 105, 234501.CrossRefGoogle Scholar
Rodgers, D. J., Servidio, S., Matthaeus, W. H., Montgomery, D. C., Mitchell, T. B. & Aziz, T. 2009 Hydrodynamic relaxation of an electron plasma to a near-maximum entropy state. Phys. Rev. Lett. 102, 244501.CrossRefGoogle ScholarPubMed
Romé, M., Cavaliere, F., Cavenago, M., Chen, S. & Maero, G. 2015 Effects of dust contamination on the transverse dynamics of a magnetized electron plasma. AIP Conf. Proc. 1668, 030001.CrossRefGoogle Scholar
Romé, M., Chen, S. & Maero, G. 2016 Wavelet characterization of 2D turbulence and intermittency in magnetized electron plasmas. Plasma Sources Sci. Technol. 25, 035016.CrossRefGoogle Scholar
Romé, M., Chen, S. & Maero, G. 2017 Structures and turbulent relaxation in non-neutral plasmas. Plasma Phys. Control. Fusion 59, 014036.CrossRefGoogle Scholar
Romé, M. & Lepreti, F. 2011 Turbulence and coherent structures in non-neutral plasmas. Eur. Phys. J. Plus 126, 38.CrossRefGoogle Scholar
Sattin, F., Scarin, P., Agostini, M., Cavazzana, R., Serianni, G., Spolaore, M. & Vianello, N. 2006 Statistical features of edge turbulence in RFX-mod from gas puffing imaging. Plasma Phys. Control. Fusion 48, 1033–1051.CrossRefGoogle Scholar
Schecter, D. A., Dubin, D. H. E., Fine, K. S. & Driscoll, C. F. 1999 Vortex crystals from 2D Euler flow: experiment and simulation. Phys. Fluids 11, 905–914.CrossRefGoogle Scholar
Spada, E., Carbone, V., Cavazzana, R., Fattorini, L., Regnoli, G., Vianello, N., Antoni, V., Martines, E., Serianni, G., Spolaore, M. et al. 2001 Search of self-organized criticality processes in magnetically confined plasmas: hints from the reversed field pinch configuration. Phys. Rev. Lett. 86, 3032–3035.CrossRefGoogle ScholarPubMed
Toufen, D. L., Pereira, F. A. C., Guimaraes, Z. O., Caldas, I. L. & Gentle, K. W. 2014 Electrostatic turbulence intermittence driven by biasing in Texas Helimak. Phys. Plasmas 21, 122302.CrossRefGoogle Scholar
Tsidulko, Yu., Pozzoli, R. & Romé, M. 2005 MEP: a 3D PIC code for the simulation of the dynamics of a non-neutral plasma. J. Comput. Phys. 209, 406–420.CrossRefGoogle Scholar
Yamada, M. & Ohkitani, K. 1991a An identification of energy cascade in turbulence by orthonormal wavelet analysis. Prog. Theor. Phys. 86, 799–815.CrossRefGoogle Scholar
Yamada, M. & Ohkitani, K. 1991b Orthonormal wavelet analysis of turbulence. Fluid Dyn. Res. 8, 101–115.CrossRefGoogle Scholar