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Magnetic axis safety factor of finite beta spheromaks and transition from spheromaks to toroidal magnetic bubbles  

Paul Bellan   Submitted: 2015-02-06 07:39

The value of the safety factor on the magnetic axis of a finite-beta spheromak is shown to be a function of beta in contrast to what was used in P. M. Bellan, Phys. Plasmas 9, 3050 (2002); this dependence on beta substantially reduces the gradient of the safety factor compared to the previous calculation. The method for generating finite-beta spheromak equilibria is extended to generate equilibria describing toroidal magnetic 'bubbles' where the hydrodynamic pressure on the magnetic axis is less than on the toroid surface. This 'anti-confinement' configuration can be considered an equilibrium with an inverted beta profile and is relevant to interplanetary magnetic clouds as these clouds have lower hydrodynamic pressure in their interior than on their surface.

Authors: Paul M. Bellan and Roberto Paccagnella
Projects: None

Publication Status: to appear in Physics of Plasmas
Last Modified: 2015-02-06 11:50
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Improved basis set for low frequency plasma waves  

Paul Bellan   Submitted: 2012-10-25 16:38

It is shown that the low frequency plasma wave equation [Stringer, Plasma Physics 5, 89(1963)] can be obtained much more directly than by the previously used method of solving for the determinant of a matrix involving the three components of the electric field vector. The more direct method uses a two-dimensional current density vector space that is precisely equivalent to the previously used three-dimensional electric field vector space. Unlike the electric field, the current density is restricted by the quasi-neutrality condition to a two-dimensional vector space. Comparison with previously obtained dispersion relations is provided and a method is presented for obtaining exact analytic solutions for the three roots of the cubic dispersion relation. The commonly used kinetic Alfvén dispersion relation is shown to be valid only for near-perpendicular propagation in a low beta plasma. It is shown that at a cross-over point where the perpendicular wave phase velocity equals the ion acoustic velocity, the coupling between Alfvén and fast modes vanishes and the Alfvén mode reverts to its cold form even in situations where the Alfvén velocity is smaller than the electron thermal velocity. A method is prescribed by which measurement of wave electric current density completely eliminates the space-time ambiguity previously believed to be an unavoidable shortcoming of single-spacecraft frequency measurements.

Authors: P. M. Bellan
Projects: None

Publication Status: accepted for publication in JGR-Space Physics
Last Modified: 2012-10-26 14:54
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Magnetically Driven Flows in Arched Plasma Structures  

Paul Bellan   Submitted: 2012-08-27 18:48

Laboratory experiments demonstrate high-speed plasma flows from both footpoints of arched magnetic flux tubes, resulting in bulk plasma transport into the flux tube and persistent axial collimation even as the flux tube lengthens and kinks. The measured flows are in agreement with the predictions of hoop force and collimation models involving fundamental MHD forces. These forces are expected to drive plasma acceleration in other open flux configurations with arched geometries, such as those found on the solar surface.

Authors: E. V. Stenson and P. M. Bellan
Projects: None

Publication Status: published in Physical Review Letters, August 13, 2012
Last Modified: 2012-08-28 12:30
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Magnetic reconnection from a multiscale instability cascade  

Paul Bellan   Submitted: 2012-02-15 21:51

Magnetic reconnection, the process whereby magnetic field lines breakand then reconnect to form a different topology, underlies criticaldynamics of magnetically confined plasmas in both natura1, andthe laboratory. Magnetic reconnection involves localizeddiffusion of the magnetic field across plasma, yet observedreconnection rates are typically much higher than can be accounted forusing classical electrical resistivity. It is generally proposedthat the field diffusion underlying fast reconnection results insteadfrom some combination of non-magnetohydrodynamic processes that becomeimportant on the 'microscopic' scale of the ion Larmor radius or theion skin depth. A recent laboratory experiment11 demonstrated atransition from slow to fast magnetic reconnection when a currentchannel narrowed to a microscopic scale, but did not address how amacroscopic magnetohydrodynamic system accesses the microscale. Recenttheoretical models and numerical simulations suggest that amacroscopic, two-dimensional magnetohydrodynamic current sheet mightdo this through a sequence of repetitive tearing and thinning intotwo-dimensional magnetized plasma structures having successively finerscales. Here we report observations demonstrating a cascade ofinstabilities from a distinct, macroscopic-scale magnetohydrodynamicinstability to a distinct, microscopic-scale (ion skin depth)instability associated with fast magnetic reconnection. Theseobservations resolve the full three-dimensional dynamics and giveinsight into the frequently impulsive nature of reconnection in spaceand laboratory plasmas.

Authors: Auna L. Moser & Paul M. Bellan
Projects: None

Publication Status: published as a Nature Letter, February 16, 2012, online on Feb 15
Last Modified: 2012-02-17 08:42
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Laboratory simulations of astrophysical jets and solar coronal loops: new results  

Paul Bellan   Submitted: 2010-01-28 16:28

An experimental program underway at Caltech has produced plasmas where the shape is neither fixed by the vacuum chamber nor fixed by an external coil set, but instead is determined by self-organization. The plasma dynamics is highly reproducible and so can be studied in considerable detail even though the morphology of the plasma is both complex and time-dependent. A surprising result has been the observation that self-collimating MHD-driven plasma jets are ubiquitous and play a fundamental role in the self-organization. The jets can be considered lab-scale simulations of astrophysical jets and in addition are intimately related to solar coronal loops. The jets are driven by the combination of the axial component of the JxB force and the axial pressure gradient resulting from the non-uniform pinch force associated with the flared axial current density. Behavior is consistent with a model showing that collimation results from axial non-uniformity of the jet velocity. In particular, flow stagnation in the jet frame compresses frozen-in azimuthal magnetic flux, squeezes together toroidal magnetic field lines, thereby amplifying the embedded toroidal magnetic field, enhancing the pinch force, and hence causing collimation of the jet.

Authors: P. M. Bellan, D. Kumar, E. V. Stenson, S. K. P. Tripathi, G. S. Yun, and A. L. Moser
Projects: None

Publication Status: AIP Conf. Proc. (submitted), paper presented at Como Italy Symposium 2009
Last Modified: 2010-01-29 09:59
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Nonequilibrium Alfvénic Plasma Jets Associated with Spheromak Formation  

Paul Bellan   Submitted: 2009-10-13 18:15

Nonequilibrium Alfvénic flows have been observed in plasma jets during the helicity injection stage of the Caltech spheromak experiment. Density and time of flight measurements of these jets show that the flows convect dense plasma because of the axial gradient in the current channel profile. A simplified MHD theory is derived to model the flow.

Authors: Deepak Kumar and Paul M. Bellan
Projects: None

Publication Status: published in Physical Review Letters, Sept 2009
Last Modified: 2009-10-14 08:00
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Observation of Kinetic Plasma Jets in a Coronal-Loop Simulation Experiment  

Paul Bellan   Submitted: 2007-02-27 16:59

Under certain conditions an intense kinetic plasma jet is observed to emerge from the apex of laboratory simulations of coronal plasma loops. Analytic and numerical models show that these jets result from a particle orbit instability in a helical magnetic field whereby magnetic forces radially eject rather than confine ions with sufficiently large counter-current axial velocity.

Authors: S. K. P. Tripathi, P. M. Bellan, and G. S. Yun
Projects: None

Publication Status: published 3/30/07: Phys. Rev. Lett. 98, 135002 (2007)
Last Modified: 2007-04-04 23:57
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Fundamentals of Plasma Physics (new textbook)  

Paul Bellan   Submitted: 2006-05-18 10:22

Publisher's blurb: Relevant to diverse plasma applications such as controlled fusion, astrophysical plasmas, solar physics, magnetospheric plasmas, and plasma thrusters, this volume exploits new powerful mathematical techniques to develop deeper insights into plasma behavior. After developing the basic plasma equations from first principles, the book explores single particle motion with particular attention to adiabatic invariance. The author then examines types of plasma waves and the issue of Landau damping. Magnet ohydrodynamic equilibrium and stability are tackled with emphasis on the topological concepts of magnetic helicity and self-organization. Advanced topics follow. Contents Preface; 1. Basic concepts; 2. The Vlasov, two-fluid, and MHD models of plasma dynamics; 3. Motion of a single plasma particle; 4. Elementary plasma waves; 5. Streaming instabilities and the Landau problem; 6. Cold plasma waves in a magnetized plasma; 7. Waves in inhomogeneous plasmas and wave energy relations; 8. Vlasov theory of warm electrostatic waves in a magnetized plasma; 9. MHD equilibria; 10. Stability of static MHD equilibria; 11. Magnetic helicity interpreted and Woltjer-Taylor relaxation; 12. Magnetic reconnection; 13. Fokker-Planck theory of collisions; 14. Wave-particle nonlinearities; 15. Wave-wave nonlinearities; 16. Non-neutral plasmas; 17. Dusty plasmas; Appendix A. Intuitive method for vector calculus identities; Appendix B. Vector calculus in orthogonal curvilinear coordinates; Appendix C. Frequently used physical constants and formulae; Bibliography; References; Index.

Authors: Paul M. Bellan
Projects: None

Publication Status: available now from Amazon.com, Cambridge University Press
Last Modified: 2006-05-18 12:26
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Dynamic and Stagnating Plasma Flow Leading to Magnetic-Flux-Tube Collimation  

Paul Bellan   Submitted: 2005-08-18 14:41

Highly collimated, plasma-filled magnetic-flux tubes are frequently observed on galactic, stellar, and laboratory scales. We propose that a single, universal magnetohydrodynamic pumping process explains why such collimated, plasma-filled magnetic-flux tubes are ubiquitous. Experimental evidence from carefully diagnosed laboratory simulations of astrophysical jets confirms this assertion and is reported here. The magnetohydrodynamic process pumps plasma into a magnetic-flux tube and the stagnation of the resulting flow causes this flux tube to become collimated.

Authors: S. You, G. S. Yun, and P. M. Bellan
Projects: None

Publication Status: published in Physical Review Letters, Vol 95, art. 45002 (July 22, 2005)
Last Modified: 2005-08-18 14:41
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Co- and counter-helicity interaction between two adjacent laboratory prominences  

Paul Bellan   Submitted: 2004-06-08 15:24

The interaction between two side-by-side solar prominence-like plasmas has been studied using a four-electrode magnetized plasma source that can impose a wide variety of surface boundary conditions. When the source is arranged to create two prominences with the same helicity (co-helicity), it is observed that helicity transfer from one prominence to the other causes the receiving prominence to erupt sooner and faster than the transmitting prominence. When the source is arranged to create two prominences with opposite helicity (counter-helicity), it is observed that upon merging, prominences wrap around each other to form closely spaced, writhing turns of plasma. This is followed by appearance of a distinct bright region in the middle and order of magnitude higher emission of soft x rays. The four-electrode device has also been used to change the angle of the neutral line and so form more pronounced S-shapes.

Authors: Hansen, J.F., Tripathi, S. K. P. and Bellan, P. M.
Projects: None

Publication Status: appeared in June 2004 Physics of Plasmas, Vol. 11, pp. 3177-3185
Last Modified: 2004-06-08 15:24
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Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result  

Paul Bellan   Submitted: 2003-01-23 09:09

It is shown that if a current-carrying magnetic flux tube is bulged at its axial midpoint z=0 and constricted at its axial endpoints z=+h,-h, then plasma will be accelerated from z=+h,-h towards z=0 resulting in a situation similar to two water jets pointed at each other. The ingested plasma convects embedded, frozen-in toroidal magnetic flux from z=+h,-h to z=0. The counter-directed flows collide and stagnate at z=0 and in so doing (i) convert their translational kinetic energy into heat, (ii) increase the plasma density at z~0, and (iii) increase the embedded toroidal flux density at z~0. The increase in toroidal flux density at z~0 increases the toroidal field Bphi and hence increases the magnetic pinch force at z~0 and so causes a reduction of the flux tube radius at z~0. Thus, the flux tube develops an axially uniform cross-section, a decreased volume, an increased density, and an increased temperature. This model is proposed as a likely hypothesis for the long-standing mystery of why solar coronal loops are observed to be axially uniform, hot, and bright. (This is a short ASCII version of abstract - no LaTex)

Authors: P. M. Bellan
Projects:

Publication Status: Physics of Plasmas (in press, to appear May 2003)
Last Modified: 2003-01-23 09:09
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Abstracts by Author
Magnetic axis safety factor of finite beta spheromaks and transition from spheromaks to toroidal magnetic bubbles
Improved basis set for low frequency plasma waves
Magnetically Driven Flows in Arched Plasma Structures
Magnetic reconnection from a multiscale instability cascade
Laboratory simulations of astrophysical jets and solar coronal loops: new results
Nonequilibrium Alfvenic Plasma Jets Associated with Spheromak Formation
Observation of Kinetic Plasma Jets in a Coronal-Loop Simulation Experiment
Fundamentals of Plasma Physics (new textbook)
Dynamic and Stagnating Plasma Flow Leading to Magnetic-Flux-Tube Collimation
Co- and counter-helicity interaction between two adjacent laboratory prominences
Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result

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