scholarly journals Bounded Solutions of Ideal MHD with Compact Support in Space-Time

Author(s):  
Daniel Faraco ◽  
Sauli Lindberg ◽  
László Székelyhidi

Abstract We show that in 3-dimensional ideal magnetohydrodynamics there exist infinitely many bounded solutions that are compactly supported in space-time and have non-trivial velocity and magnetic fields. The solutions violate conservation of total energy and cross helicity, but preserve magnetic helicity. For the 2-dimensional case we show that, in contrast, no nontrivial compactly supported solutions exist in the energy space.

2020 ◽  
Vol 495 (4) ◽  
pp. 3795-3806 ◽  
Author(s):  
James Wurster ◽  
Benjamin T Lewis

ABSTRACT Non-ideal magnetohydrodynamics (MHD) is the dominant process. We investigate the effect of magnetic fields (ideal and non-ideal) and turbulence (sub- and transsonic) on the formation of circumstellar discs that form nearly simultaneously with the formation of the protostar. This is done by modelling the gravitational collapse of a 1 M⊙ gas cloud that is threaded with a magnetic field and imposed with both rotational and turbulent velocities. We investigate magnetic fields that are parallel/antiparallel and perpendicular to the rotation axis, two rotation rates, and four Mach numbers. Disc formation occurs preferentially in the models that include non-ideal MHD where the magnetic field is antiparallel or perpendicular to the rotation axis. This is independent of the initial rotation rate and level of turbulence, suggesting that subsonic turbulence plays a minimal role in influencing the formation of discs. Aside from first core outflows that are influenced by the initial level of turbulence, non-ideal MHD processes are more important than turbulent processes during the formation of discs around low-mass stars.


2020 ◽  
Vol 495 (4) ◽  
pp. 3807-3818 ◽  
Author(s):  
James Wurster ◽  
Benjamin T Lewis

ABSTRACT Non-ideal magnetohydrodynamics (MHD) is the dominant process. We investigate the effect of magnetic fields (ideal and non-ideal) and turbulence (sub- and transsonic) on the formation of protostars by following the gravitational collapse of 1 M⊙ gas clouds through the first hydrostatic core to stellar densities. The clouds are imposed with both rotational and turbulent velocities, and are threaded with a magnetic field that is parallel/antiparallel or perpendicular to the rotation axis; we investigate two rotation rates and four Mach numbers. The initial radius and mass of the stellar core are only weakly dependent on the initial parameters. In the models that include ideal MHD, the magnetic field strength implanted in the protostar at birth is much higher than observed, independent of the initial level of turbulence; only non-ideal MHD can reduce this strength to near or below the observed levels. This suggests that not only is ideal MHD an incomplete picture of star formation, but that the magnetic fields in low mass stars are implanted later in life by a dynamo process. Non-ideal MHD suppresses magnetically launched stellar core outflows, but turbulence permits thermally launched outflows to form a few years after stellar core formation.


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.


1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.


Author(s):  
Eduardo Lascas Neto ◽  
Jonathan P Graves ◽  
Madhusudan Raghunathan ◽  
Cristian Sommariva ◽  
David Pfefferlé

Abstract Strongly peaked tungsten accumulation is a common feature of high performance plasma scenarios in JET with the ITER-like wall, particularly during MHD activity induced by m⁄n = 1⁄1 continuous modes. This study investigates the effect of 1⁄1 long living internal kink modes on heavy impurity transport in the presence of strong flows and NTV ambipolar electric field. A novel formulation which includes these effects is presented and applied in the VENUS-LEVIS code in order to follow tungsten ions in a saturated JET-like 1⁄1 internal kinked toroidally rotating plasma configuration. The synergy between 3D magnetic fields, strong flows and NTV is seen to cause tungsten accumulation in contrast to what is observed in similar axisymmetric configurations. Rapid inward transport of impurities in JET plasmas following the triggering of continuous 1⁄1 modes is explained by the work presented here, and we use the same theory to postulate why outward transport can occur in kinked ASDEX-U plasmas.


2021 ◽  
Vol 62 ◽  
pp. 29-52
Author(s):  
Ying-Qiu Gu ◽  

In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $\Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time corresponds to the simplest and best case. Besides, the relation between the curvilinear coordinate frame and the local orthonormal basis in the curved space-time is discussed in detail, the covariant derivatives of the spinor and tensors are derived, and the connection of the orthogonal basis in tangent space is calculated. These results are helpful for both theoretical analysis and practical calculation. The basis matrices are the faithful representation of Clifford algebras in any $p+q$ dimensional Minkowski space-time or Riemann space, and the Clifford calculus converts the complicated relations in geometry and physics into simple and concise algebraic operations. Clifford numbers over any number field $\mathbb{F}$ expressed by this matrix basis form a well-defined $2^n$ dimensional hypercomplex number system. Therefore, we can expect that Clifford algebras will complete a large synthesis in science.


2018 ◽  
Vol 6 ◽  
Author(s):  
TIMOTHY CANDY ◽  
SEBASTIAN HERR

We consider the global behaviour for large solutions of the Dirac–Klein–Gordon system in critical spaces in dimension $1+3$. In particular, we show that bounded solutions exist globally in time and scatter, provided that a controlling space–time Lebesgue norm is finite. A crucial step is to prove nonlinear estimates that exploit the dichotomy between transversality and null structure, and furthermore involve the controlling norm.


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