scholarly journals Proton imaging of stochastic magnetic fields

2017 ◽  
Vol 83 (6) ◽  
Author(s):  
A. F. A. Bott ◽  
C. Graziani ◽  
P. Tzeferacos ◽  
T. G. White ◽  
D. Q. Lamb ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Magnetic Fields ◽  
Flux Distribution ◽  
Magnetic Energy ◽  
Relative Size ◽  
Proton Flux ◽  
Nonlinear Behaviour ◽  
Stochastic Field ◽  
Stochastic Magnetic Fields

Recent laser-plasma experiments (Foxet al.,Phys. Rev. Lett., vol. 111, 2013, 225002; Huntingtonet al.,Nat. Phys., vol. 11(2), 2015, 173–176; Tzeferacoset al.,Phys. Plasmas, vol. 24(4), 2017a, 041404; Tzeferacoset al., 2017b,arXiv:1702.03016[physics.plasm-ph]) report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a proton-imaging diagnostic can be used to determine a range of relevant magnetic-field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. This ‘Kugland image-flux relation’ was previously derived (Kuglandet al., Rev. Sci. Instrum.vol. 83(10), 2012, 101301) under simplifying assumptions typically valid in actual proton-imaging set-ups. We conclude that, as with regular electromagnetic fields, features of the beam’s final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter – the contrast parameter$\unicode[STIX]{x1D707}\equiv d_{s}/{\mathcal{M}}l_{B}$– which quantifies the relative size of the correlation length$l_{B}$of the stochastic field, proton displacements$d_{s}$due to magnetic deflections and the image magnification${\mathcal{M}}$. For stochastic magnetic fields, we establish the existence of four contrast regimes, under which proton-flux images relate to their parent fields in a qualitatively distinct manner. These are linear, nonlinear injective, caustic and diffusive. The diffusive regime is newly identified and characterised. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the path-integrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magnetic-energy spectrum can be obtained under a further statistical assumption of isotropy. This is not the case in the caustic or diffusive regimes. We discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one’s ability to extract magnetic-field statistics. The results presented in this paper are of consequence in providing a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of proton-flux images.

scholarly journals The measurement of the energy of cosmic rays - II—The curvature measurements and the energy spectrum

1936 ◽  
Vol 154 (883) ◽  
pp. 573-587 ◽  
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Cosmic Rays ◽  
Magnetic Fields ◽  
Strong Magnetic Fields ◽  
The Earth ◽  
Primary Particles ◽  
Curvature Measurements

Both the penetrating power of the cosmic rays through material ab­sorbers and their ability to reach the earth in spite of its magnetic field, make it certain that the energy of many of the primary particles must reach at least 10 11 e-volts. However, the energy measurements by Kunze, and by Anderson, using cloud chambers in strong magnetic fields, have extended only to about 5 x 10 9 e-volts. Particles of greater energy were reported, but the curvature of their tracks was too small to be measured with certainty. We have extended these energy measurements to somewhat higher energies, using a large electro-magnet specially built for the purpose and described in Part I. As used in these experiments, the magnet allowed the photography of tracks 17 cm long in a field of about 14,000 gauss. The magnet weighed about 11,000 kilos and used a power of 25 kilowatts.

scholarly journals Are the photospheric sunspots magnetically force-free in nature?

2010 ◽  
Vol 6 (S273) ◽  
pp. 333-337 ◽  
Author(s):  
Sanjiv Kumar Tiwari
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Sufficient Conditions ◽  
Field Measurements ◽  
Magnetic Behaviour ◽  
Optical Telescope ◽  
Energy Gradient ◽  
Necessary And Sufficient

AbstractIn a force-free magnetic field, there is no interaction of field and the plasma in the surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of many magnetic parameters like magnetic energy, gradient of twist of sunspot magnetic fields (computed from the force-free parameter α), including any kind of extrapolations heavily hinge on the force-free approximation of the photospheric magnetic fields. The force-free magnetic behaviour of the photospheric sunspot fields has been examined by Metcalf et al. (1995) and Moon et al. (2002) ending with inconsistent results. Metcalf et al. (1995) concluded that the photospheric magnetic fields are far from the force-free nature whereas Moon et al. (2002) found the that the photospheric magnetic fields are not so far from the force-free nature as conventionally regarded. The accurate photospheric vector field measurements with high resolution are needed to examine the force-free nature of sunspots. We use high resolution vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard Hinode to inspect the force-free behaviour of the photospheric sunspot magnetic fields. Both the necessary and sufficient conditions for force-freeness are examined by checking global as well as as local nature of sunspot magnetic fields. We find that the sunspot magnetic fields are very close to the force-free approximation, although they are not completely force-free on the photosphere.

On the spontaneous magnetic field in a conducting liquid in turbulent motion

1950 ◽  
Vol 201 (1066) ◽  
pp. 405-416 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Turbulent Motion ◽  
Small Scale ◽  
Flow Equations ◽  
Metallic Conductor ◽  
Set Up ◽  
The Stability ◽  
The Magnetic Field

Several recent investigations in geophysics and astrophysics have involved a consideration of the hydrodynamics of a fluid which is a good electrical conductor. In this paper one of the problems which seem likely to arise in such investigations is discussed. The fluid is assumed to be incompressible and in homogeneous turbulent motion, and externally imposed electric and magnetic fields are assumed to be absent. The equations governing the interaction of the electromagnetic field and the turbulent motion are set up with the same assumptions as are used to obtain the Maxwell and current flow equations for a metallic conductor. It is shown that the equation for the magnetic field is identical in form with that for the vorticity in a non-conducting fluid; immediate deductions are that lines of magnetic force move with the fluid when the conductivity is infinite, and that the small-scale components of the turbulence have the more powerful effect on the magnetic field. The first question considered is the stability of a purely hydrodynamical system to small disturbing magnetic fields, and it is shown that the magnetic energy of the disturbance will increase provided the conductivity is greater than a critical value determined by the viscosity of the fluid. The rate of growth of magnetic energy is approximately exponential, with a doubling time which can be simply related to the properties of the turbulence. General mechanical considerations suggest that a steady state is reached when the magnetic field has as much energy as is contained in the small-scale components of the turbulence. Estimates of this amount of energy and of the region of the spectrum in which it will lie are given in terms of observable properties of the turbulence.

scholarly journals Tunnel Magnetoresistance of Fe3O4/MgO/Fe Nanostructures

2011 ◽  
Vol 2011 ◽  
pp. 1-3
Author(s):  
S. G. Chigarev ◽  
E. M. Epshtein ◽  
I. V. Malikov ◽  
G. M. Mikhailov ◽  
P. E. Zilberman
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Tunnel Junction ◽  
Magnetic Energy ◽  
Magnetic Tunnel Junction ◽  
Tunnel Magnetoresistance ◽  
Unidirectional Anisotropy ◽  
Layer Orientation ◽  
Layer Magnetization

A magnetic tunnel junction Fe3O4/MgO/Fe with (001) layer orientation is considered. The junction magnetic energy is analyzed as a function of the angle between the layer magnetization vectors under various magnetic fields. The tunnel magnetoresistance is calculated as a function of the external magnetic field. In contrast with junctions with unidirectional anisotropy, a substantially lower magnetic field is required for the junction switching.

scholarly journals Why fast magnetic reconnection is so prevalent

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Allen H. Boozer
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Reconnection ◽  
Large Scale ◽  
Magnetic Energy ◽  
Recognition Theory ◽  
Coordinate Model ◽  
Field Lines ◽  
Large Scale Flow ◽  
Analogous Effect

Evolving magnetic fields are shown to generically reach a state of fast magnetic reconnection in which magnetic field line connections change and magnetic energy is released at an Alfvénic rate. This occurs even in plasmas with zero resistivity; only the finiteness of the mass of the lightest charged particle, an electron, is required. The speed and prevalence of Alfvénic or fast magnetic reconnection imply that its cause must be contained within the ideal evolution equation for magnetic fields, $\unicode[STIX]{x2202}\boldsymbol{B}/\unicode[STIX]{x2202}t=\unicode[STIX]{x1D735}\times (\boldsymbol{u}\times \boldsymbol{B})$, where $\boldsymbol{u}(\boldsymbol{x},t)$ is the velocity of the magnetic field lines. For a generic $\boldsymbol{u}(\boldsymbol{x},t)$, neighbouring magnetic field lines develop a separation that increases exponentially, as $e^{\unicode[STIX]{x1D70E}(\ell ,t)}$ with $\ell$ the distance along a line. This exponentially enhances the sensitivity of the evolution to non-ideal effects. An analogous effect, the importance of stirring to produce a large-scale flow and enhance mixing, has been recognized by cooks through many millennia, but the importance of the large-scale flow $\boldsymbol{u}$ to reconnection is customarily ignored. In part this is due to the sixty-year focus of recognition theory on two-coordinate models, which eliminate the exponential enhancement that is generic with three coordinates. A simple three-coordinate model is developed, which could be used to address many unanswered questions.

scholarly journals Turbulent dynamo in a collisionless plasma

2016 ◽  
Vol 113 (15) ◽  
pp. 3950-3953 ◽  
Author(s):  
François Rincon ◽  
Francesco Califano ◽  
Alexander A. Schekochihin ◽  
Francesco Valentini
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Collisionless Plasma ◽  
High Energy ◽  
Nearby Galaxy ◽  
Astrophysical Plasmas ◽  
Flow Energy ◽  
Field Amplification ◽  
Turbulent Dynamo

Magnetic fields pervade the entire universe and affect the formation and evolution of astrophysical systems from cosmological to planetary scales. The generation and dynamical amplification of extragalactic magnetic fields through cosmic times (up to microgauss levels reported in nearby galaxy clusters, near equipartition with kinetic energy of plasma motions, and on scales of at least tens of kiloparsecs) are major puzzles largely unconstrained by observations. A dynamo effect converting kinetic flow energy into magnetic energy is often invoked in that context; however, extragalactic plasmas are weakly collisional (as opposed to magnetohydrodynamic fluids), and whether magnetic field growth and sustainment through an efficient turbulent dynamo instability are possible in such plasmas is not established. Fully kinetic numerical simulations of the Vlasov equation in a 6D-phase space necessary to answer this question have, until recently, remained beyond computational capabilities. Here, we show by means of such simulations that magnetic field amplification by dynamo instability does occur in a stochastically driven, nonrelativistic subsonic flow of initially unmagnetized collisionless plasma. We also find that the dynamo self-accelerates and becomes entangled with kinetic instabilities as magnetization increases. The results suggest that such a plasma dynamo may be realizable in laboratory experiments, support the idea that intracluster medium turbulence may have significantly contributed to the amplification of cluster magnetic fields up to near-equipartition levels on a timescale shorter than the Hubble time, and emphasize the crucial role of multiscale kinetic physics in high-energy astrophysical plasmas.

scholarly journals Magnetic field generation, Weibel-mediated collisionless shocks, and magnetic reconnection in colliding laser-produced plasmas

2015 ◽  
Vol 11 (A29A) ◽  
pp. 329-332
Author(s):  
W. Fox ◽  
A. Bhattacharjee ◽  
G. Fiksel
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Reconnection ◽  
Magnetic Energy ◽  
Cosmic Ray ◽  
Laboratory Astrophysics ◽  
Shock Acceleration ◽  
Shock Formation ◽  
Magnetic Field Generation ◽  
Temperature Plasma

AbstractColliding plasmas are ubiquitous in astrophysical environments and allow conversion of kinetic energy into heat and, most importantly, the acceleration of particles to extremely high energies to form the cosmic ray spectrum. In collisionless astrophysical plasmas, kinetic plasma processes govern the interaction and particle acceleration processes, including shock formation, self-generation of magnetic fields by kinetic plasma instabilities, and magnetic field compression and reconnection. How each of these contribute to the observed spectra of cosmic rays is not fully understood, in particular both shock acceleration processes and magnetic reconnection have been proposed. We will review recent results of laboratory astrophysics experiments conducted at high-power, inertial-fusion-class laser facilities, which have uncovered significant results relevant to these processes. Recent experiments have now observed the long-sought Weibel instability between two interpenetrating high temperature plasma plumes, which has been proposed to generate the magnetic field necessary for shock formation in unmagnetized regimes. Secondly, magnetic reconnection has been studied in systems of colliding plasmas using either self-generated magnetic fields or externally applied magnetic fields, and show extremely fast reconnection rates, indicating fast destruction of magnetic energy and further possibilities to accelerate particles. Finally, we highlight kinetic plasma simulations, which have proven to be essential tools in the design and interpretation of these experiments.

Plasma transport in stochastic magnetic fields. Part 3. Kinetics of test particle diffusion

1983 ◽  
Vol 30 (1) ◽  
pp. 11-56 ◽  
Author(s):  
John A. Krommes ◽  
Carl Oberman ◽  
Robert G. Kleva
Keyword(s):  
Magnetic Fields ◽  
Test Particle ◽  
Scaling Laws ◽  
Direct Interaction ◽  
Stochastic Field ◽  
Common Procedure ◽  
Correlation Lengths ◽  
Direct Interaction Approximation ◽  
Stochastic Magnetic Fields ◽  
Autocorrelation Length

A discussion is given of test particle transport in the presence of specified stochastic magnetic fields, with particular emphasis on the collisional limit. Certain paradoxes and inconsistencies in the literature regarding the form of the scaling laws are resolved by carefully distinguishing a number of physically distinct correlation lengths, and thus identifying several collisional subregimes. The common procedure of averaging the conventional fluid equations over the statistics of a random field is shown to fail in some important cases because of breakdown of the Chapman-Enskog ordering in the presence of a stochastic field component with short autocorrelation length. A modified perturbation theory is introduced which leads to a Kubo-like formula valid in all collisional regimes. The direct-interaction approximation is shown to fail in the interesting limit in which the orbit exponentiation length LK appears explicitly. A higher-order renormalized kinetic theory in which LK appears naturally is discussed and used to rederive more systematically the results of the heuristic scaling arguments.

The Magnetic Fields of Pulsars, Electrons and the Sun

1992 ◽  
Vol 10 (2) ◽  
pp. 110-112
Author(s):  
K. D. Cole
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Rest Mass ◽  
Building Blocks ◽  
Polar Regions ◽  
The Sun ◽  
Electron Positron ◽  
Celestial Bodies ◽  
Electron Gyrofrequency

AbstractAn apparent connection is reported between the magnetic field strengths inside an electron, in newly born pulsars, and the sun. It is argued that the upper limit to the strength of magnetic field which seems to exist is that which would permit emission of a photon at the non-relativistic electron gyrofrequency, with energy of the order of the electron rest mass. The strongest magnetic fields at the surface of polar regions of pulsars conform to this. By equating approximately the rest mass of an electron to its magnetic energy, the same magnetic field is found inside the electron. It is proposed that magnetic field building ‘blocks’ called M-particles are formed by a variant of the electron-positron spin-zero annihilation. The particles become as tightly stacked as possible to form the macroscopic magnetic field of the newly born pulsar. The sun’s present magnetic moment is described by a pulsar-sized object at its centre, with the maximum packing of M-particles. The hypothesis may have a bearing on the formation of magnetic fields in celestial bodies, and on the secular variation of the magnetic fields of the sun and the Earth.

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