scholarly journals The path of an electron in combined radial magnetic and electric fields

1. In the course of an investigation with a focus tube, in which the anti-cathode was a magnetic pole, some interesting observations were made with regard to the distribution of the fluorescence on the walls of the tube as the magnetic field varied. In order to explain the changes observed, the path of an electron in a radial field was investigated mathematically, and was found to lie on a right circular cone whose vertex coincides with the magnetic pole. If the surface of the cone is developed into a plane the trace of the path is a conic section, with the vertex as focus. This result continues to hold when an electric field, with its lines of force radiating from the same point, is superposed on the magnetic field. Although the actual distribution of electric intensity in a highly exhausted tube must differ widely from that here considered, the investigation sufficiently explains the facts observed. Theoretical . 2. The object is to find the path of a particle of mass m carrying a charge e in combined magnetic and electric fields, when the lines of force are radial and are such as might be due to a single pole of strength μ coincident with an electric charge k .

2016 ◽  
Vol 34 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A. D. M. Walker ◽  
G. J. Sofko

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.


2007 ◽  
Vol 21 (10) ◽  
pp. 1715-1720 ◽  
Author(s):  
NANA METREVELI ◽  
ZAUR KACHLISHVILI ◽  
BEKA BOCHORISHVILI

The transverse runaway (TR) is a phenomenon whereby for a certain combination of energy and momentum scattering mechanisms of hot electrons, and for a certain threshold of the applied electric field, the internal (total) field tends to infinity. In this work, the effect of the magnetic field on the transverse runaway threshold is considered. It is shown that with increasing magnetic field, the applied critical electric fields relevant to TR decrease. The obtained results are important for practical applications of the TR effect as well as for the investigation of possible nonlinear oscillations that may occur near the TR threshold.


2007 ◽  
Vol 25 (3) ◽  
pp. 453-464 ◽  
Author(s):  
L. Torrisi ◽  
D. Margarone ◽  
S. Gammino ◽  
L. Andò

Laser-generated plasma is obtained in high vacuum (10−7 mbar) by irradiation of metallic targets (Al, Cu, Ta) with laser beam with intensities of the order of 1010 W/cm2. An Nd:Yag laser operating at 1064 nm wavelength, 9 ns pulse width, and 500 mJ maximum pulse energy is used. Time of flight measurements of ion emission along the direction normal to the target surface were performed with an ion collector. Measurements with and without a 0.1 Tesla magnetic field, directed along the normal to the target surface, have been taken for different target-detector distances and for increasing laser pulse intensity. Results have demonstrated that the magnetic field configuration creates an electron trap in front of the target surface along the axial direction. Electric fields inside the trap induce ion acceleration; the presence of electron bundles not only focuses the ion beam but also increases its energy, mean charge state and current. The explanation of this phenomenon can be found in the electric field modification inside the non-equilibrium plasma because of an electron bunching that increases the number of electron-ion interactions. The magnetic field, in fact, modifies the electric field due to the charge separation between the clouds of fast electrons, many of which remain trapped in the magnetic hole, and slow ions, ejected from the ablated target; moreover it increases the number of electron-ion interactions producing higher charge states.


1970 ◽  
Vol 4 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Barbara Abraham-Shrauner

Suppression of runaway of electrons in a weak, uniform electric field in a fully ionized Lorentz plasma by crossed magnetic and electric fields is analysed. A uniform, constant magnetic field parallel to a constant or harmonically time varying electric field does not alter runaway from that in the absence of the magnetic field. For crossed, constant fields the passage to runaway or to free motion as described by constant drift motion and spiral motion about the magnetic field is lengthened in time for strong magnetic fields. The new ‘runaway’ time scale is roughly the ratio of the cyclotron frequency to the collision frequency squared for cyclotron frequencies much greater than the collision frequency. All ‘runaway’ time scales may be given approximately by t2E Teff where tE is the characteristic time of the electric field and Teff is the ffective collision time as estimated from the appropriate component of the electrical conductivity.


2007 ◽  
Vol 21 (08n09) ◽  
pp. 1594-1599 ◽  
Author(s):  
M. P. TELENKOV ◽  
YU. A. MITYAGIN

The transverse resonant tunneling transport and electric field domain formation in GaAs/AlGaAs superlattices were investigated in a strong tilted magnetic field. The magnetic field component parallel to structure layers causes intensive tunneling transition between Landau levels with Δn≠0, resulting in the considerable "inhomogeneous" broadening of intersubband tunneling resonance as well as in the shift of the resonance toward higher electric fields. This leads to noticeable changes of the I-V characteristics of the superlattice, namely to smoothing of the periodic NDC structure on plateau-like regions caused by formation of the electric field domains and to the shift of the plateaus toward the higher applied voltage. The predicted behavior of the I-V characteristics of the structures in magnetic field was found experimentally.


2018 ◽  
Vol 36 (2) ◽  
pp. 373-379 ◽  
Author(s):  
Song Fu ◽  
Shiyong Huang ◽  
Meng Zhou ◽  
Binbin Ni ◽  
Xiaohua Deng

Abstract. It has been shown that the guide field substantially modifies the structure of the reconnection layer. For instance, the Hall magnetic and electric fields are distorted in guide field reconnection compared to reconnection without guide fields (i.e., anti-parallel reconnection). In this paper, we performed 2.5-D electromagnetic full particle simulation to study the electric field structures in magnetic reconnection under different initial guide fields (Bg). Once the amplitude of a guide field exceeds 0.3 times the asymptotic magnetic field B0, the traditional bipolar Hall electric field is clearly replaced by a tripolar electric field, which consists of a newly emerged electric field and the bipolar Hall electric field. The newly emerged electric field is a convective electric field about one ion inertial length away from the neutral sheet. It arises from the disappearance of the Hall electric field due to the substantial modification of the magnetic field and electric current by the imposed guide field. The peak magnitude of this new electric field increases linearly with the increment of guide field strength. Possible applications of these results to space observations are also discussed. Keywords. Space plasma physics (magnetic reconnection)


2007 ◽  
Vol 25 (2) ◽  
pp. 543-555 ◽  
Author(s):  
J. D. Menietti ◽  
R. A. Frahm ◽  
A. Korth ◽  
F. S. Mozer ◽  
Y. Khotyaintsev

Abstract. We investigate particle and fields data during a conjunction of the Polar and Cluster spacecraft. This conjunction occurs near the dayside cusp boundary layer when a dayside inverted-V was observed in the particle data of both satellites. Electron, ion, electric field, and magnetic field data from each satellite confirm that the dayside inverted-V (DSIV) structure is present at the location of both satellites and the electric fields persist from the altitude of the Polar (lower) spacecraft to the altitude of the Cluster spacecraft. We observe accelerated, precipitating electrons and upward ions along the magnetic field. In addition, large amplitude electric fields perpendicular to the ambient magnetic field seen by Polar and by Cluster suggest significant parallel electric fields associated with these events. For similar DSIV events observed by the Polar spacecraft, plasma waves (identified as possible Alfvén waves) have been observed to propagate in both directions along the magnetic field line. Future conjunctions will be necessary to confirm that DSIVs are associated with reconnection sites.


2000 ◽  
Vol 195 ◽  
pp. 311-312
Author(s):  
Y. E. Litvinenko

Fast magnetic reconnection in extragalactic jets leads to electron acceleration by the DC electric field in the reconnecting current sheet. The maximum electron energy (γ > 106) and the acceleration time (< 106 s) are determined by the magnetic field dynamics in the sheet.


A theory of the aurora polaris is proposed which attempts to explain many features of the complicated morphology of auroral displays. One basis of the theory is the presence, during magnetic disturbance, of additional or enhanced magnetic fields due to electric currents within a distance of several earth radii from the earth’s centre. One such field (denoted by DCF) is due to electric currents flowing near the inner surface of the solar stream that then envelopes the earth. A hollow is carved in the stream by the geomagnetic field. The other field (denoted by DR) is that of an electric ring current, additional or enhanced, that flows westward round the earth. This is carried by the particles of the Van Allen belts. A third field (denoted by DP) is that of the disturbance currents that flow in the ionosphere, under the impulsion of electromotive forces generated mainly in polar regions. We consider it likely that during magnetic storms and auroral displays, neutral lines appear in the magnetic field near the earth. These will lie mainly on the dark side of the earth, in or near the equatorial plane, on the nearer side of the ring current. At times these lines may extend over more than 180° of longitude, so that a part of them may lie on the sunward side of the earth. These neutral lines are of two types, which we call O and X they appear together, in pairs. During disturbed conditions there may be more than one pair. Lines of force cross at points on X neutral lines, but they do not pass through O neutral lines. As Dungey has shown, charged particles will tend to be concentrated near X points (of which the X neutral lines are the locus). Charges drawn toward the neutral line will be discharged into the earth’s atmosphere along the lines of magnetic force. We suggest that the location, nature and motions of the auroral forms are determined by the position, form and motion of the X neutral lines, lying in or near the plane of the geomagnetic equator. It seems necessary to suppose, in addition, that an electric field arises sporadically along the X lines. When this is absent, the aurora appears as a quiet arc. The onset of the suggested electric field concentrates the charges more narrowly near the X line and near the lines of force that extend from it to the auroral zone. This produces extremely thin-rayed auroral arcs. The above concentration of electrons near an X neutral line produces a large flux of electrons, while the proton flux is diminished. A dynamical instability due to this flux difference (the space charge density is supposed to be very small) produces a slight separation of protons and electrons along and near the lines of force through the X line. Hence in the auroral ionosphere there is an associated electric field. This is usually directed towards the equator. It drives electric current, usually westward, along the auroral zones, and produces the strong magnetic disturbances (DP) there observed. Birkeland called these polar elementary storms. The rapid auroral changes are ascribed to instabilities of the magnetic field in the region near the X line or lines, to the rear of the earth, where the resultant magnetic field is weak. The ray structure in the auroral arc is ascribed to an instability of the thin sheet of electron flow. Cosmic rockets have shown that the magnetic field, up to and beyond ten earth radii, departs from the values corresponding to the internally produced main geomagnetic field. As yet these explorations do not seem to have disclosed the existence of reversals of the field in or near the magnetic equatorial plane. But on the basis of our auroral hypothesis, we predict with considerable confidence that such reversals will be found to occur, on the dark side of the earth, during great auroral displays. The theory here proposed is discussed in connexion with recent I. G. Y. and I. G. C. auroral, magnetic and other data.


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