A theorem on MHD-instability of plasmas with resistive walls

1971 ◽  
Vol 11 (3) ◽  
pp. 259-260 ◽  
Author(s):  
D. Pfirsch ◽  
H. Tasso
Keyword(s):  
Solar Physics ◽  
2021 ◽  
Vol 296 (8) ◽  
Author(s):  
J. Threlfall ◽  
J. Reid ◽  
A. W. Hood

AbstractMagnetohydrodynamic (MHD) instabilities allow energy to be released from stressed magnetic fields, commonly modelled in cylindrical flux tubes linking parallel planes, but, more recently, also in curved arcades containing flux tubes with both footpoints in the same photospheric plane. Uncurved cylindrical flux tubes containing multiple individual threads have been shown to be capable of sustaining an MHD avalanche, whereby a single unstable thread can destabilise many. We examine the properties of multi-threaded coronal loops, wherein each thread is created by photospheric driving in a realistic, curved coronal arcade structure (with both footpoints of each thread in the same plane). We use three-dimensional MHD simulations to study the evolution of single- and multi-threaded coronal loops, which become unstable and reconnect, while varying the driving velocity of individual threads. Experiments containing a single thread destabilise in a manner indicative of an ideal MHD instability and consistent with previous examples in the literature. The introduction of additional threads modifies this picture, with aspects of the model geometry and relative driving speeds of individual threads affecting the ability of any thread to destabilise others. In both single- and multi-threaded cases, continuous driving of the remnants of disrupted threads produces secondary, aperiodic bursts of energetic release.


Author(s):  
N.P. Savenkova ◽  
A.Yu. Mokin ◽  
N.S. Udovichenko

Mathematical simulation of industrial aluminium electrolytic cell operation allows us to predict and indicate the causes of magnetohydrodynamic (MHD) instability and bath level skewing, as well as investigate other features of the aluminium electrolysis process. In order to analyse the MHD stability of the electrolytic cell, we adapted a three-dimensional mathematical model that uses a multi-phase approach to describing the media (aluminium, electrolyte and gas) and treats the hydrodynamic, electromagnetic, thermal and electrochemical processes in the bath as interrelated. Our test calculations confirmed that the model is adequate and that the numerical solution proposed converges with sufficient accuracy. The paper describes our numerical investigation results concerning MHD stability of a multi-anode electrolytic cell when its thermal conditions and working space shape configuration change; our simulation included the metal-electrolyte phase interfaces and took into account the MHD instability developing when replacing burnt-out anodes. We estimated how various initial crust configurations affect the MHD stability. We investigated how the process parameters affect the working space shape in the bath, which is a dynamic object, same as the metal-electrolyte interface and the reverse oxidation zone surface. We specifically studied the way changes in potential affect the MHD stable shape of the working space in the bath. We show that varying the potential between any given pair of anodes can change the shape of the working space, that is, crust melts as potential increases, while lowering potential leads to further accretion. As this happens, we note that there is an increase in the vibration magnitudes of the liquid metal and the lower reverse oxidation zone boundary, but these variations are still within the range acceptable in terms of MHD stability of the electrolysis process


2007 ◽  
Vol 33 (2) ◽  
pp. 81-90 ◽  
Author(s):  
M. I. Patrov ◽  
S. E. Bender ◽  
V. K. Gusev ◽  
D. É. Kravtsov ◽  
I. A. Mironov ◽  
...  

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