Nonadiabatic Motion Research Articles

Plasma heating and compression when nonadiabatic motion of particles

The motion of charged particles in axisymmetric quickly increasing uniform magnetic field is considered. The class of fields in which particles energy increases as H 2 is determined. After the field ceases its increase all particles simultaneously reach the field axis.

Adiabaticity of Charged-Particle Trajectories in a Cusped Magnetic Field

The region of adiabatic charged-particle motion for a spindle-cusp field is determined on the basis of confinement times both by numerical integration of the particle orbits and by an experiment utilizing electrons. If the critical flux line dividing the adiabatic and nonadiabatic regions is expressed in Grad's form, ψc = (aλ0)3, where λ0 is the cyclotron radius of the particle corresponding to its total velocity, the numerical analysis yields a value for the constant a of 3.5–4.2 and the experiment yields a = 4.36. It is further shown that the transition zone between the regions of adiabatic and nonadiabatic motion is about two-thirds of an electron cyclotron radius in width, and that the relative field variation encountered during one cyclotron period by an electron whose guiding center is located in this zone is between 11 and 19%. A random-walk model of particle motion, based on the near noncorrelation between fluctuations of the magnetic moment on successive traversals of the field, is used to calculate the effect on particle lifetime of the location of the first reflection point, and thereby explain the apparently excessive random scatter of the data.

An approximate calculation of the non-adiabatic motion of a charged particle in an inhomogeneous rotationally symmetric magnetic field

A study is made of the motion of a particle injected longitudinally into a rotationally symmetric magnetic field increasing linearly in an arbitrarily sharp way on the axis of symmetry. By expanding the magnetic potential in a series in the vicinity of the line of force from which the particle starts, and by restricting our considerations to linear terms, we arrive at a single linearized equation of motion for the radial motion, as we assume the longitudinal motion to be uniform. The linearized equation can be solved exactly. Numerical evaluation is carried out (with the linearized line of force) for several different slopes of the field, and compared for similar cases with a numerical evaluation of an exact nonlinear problem. The method described in the paper can also be applied to cases with more general initial conditions, when the particle also moves with an azimuthal velocity.

Non-adiabatic motion of a particle in a cusped magnetic field

Non-adiabatic motion of a particle in a cusped magnetic field

Non-adiabatic motion of a particle in a cusped magnetic field

Particle orbits in a counter Helmholtz field have been investigated, both analytically and by means of a digital computer. The results give information about the containment time of a particle, the density distribution of particles within the Stormer regions, and particle reflection in the r- and z-mirrors. The containment time of 10 keV H+-ions in a cusped field of 400 G/cm is 5 μsec, corresponding to an average density of 9 × 105 cm-3/mA injected current. Locally the density will be higher, due to a radial density dependence which is found statistically. A pseudo-magnetic moment gives a good prediction of the reflection point in the r- and z-mirrors. The orthodox magnetic moment is less good in this respect. The implications of the computer results for an injection experiment in a cusped magnetic field are discussed.

Nonadiabatic Motion of a Charged Particle in an Axisymmetric Magnetic Barrier

A study was made of the motion of a single charged particle in the magnetic induction generated by an axisymmetric current sheet, the current of which was sinusoidally modulated along the axis. Several adiabatically invariant quantities were investigated, and it was found that M4 = |v×B|2/|B|3 varied least along a given trajectory. A particle was considered to be adiabatic if M4 varied by less than 5% during a single interaction with the magnetic barrier. An averaging process was found which made it possible to predict the relations between particle mass and energy, and the magnetic induction strength and geometry, which cause M4 to vary by more than 5% during a single interaction with the magnetic barrier. Experimental apparatus was constructed which made it possible to study a single interaction of a beam of charged particles with a magnetic barrier under steady-state conditions. An experimental procedure was developed which made it possible to detect the transition from adiabatic to nonadiabatic reflection of the ion beam, and the results were compared with the results of the numerical computation.

Non-adiabatic motion of charged particles traversing a weak magnetic field: Pitch angle scattering

A charged particle moves with velocityv in a constant non-uniform magnetic fieldH, spiralling with Larmor radiusR. IfR is small compared with the scale lengthL of the field, the magnetic moment associated with the Larmor motion of the particle is nearly constant. Consequently θ, the (‘pitch’) angle betweenv andH, varies as arcsinH1/2. Hence θ in such adiabatic motion is approximately the same at points on the path whereH has the same value. But the magnetic moment and the pitch angle may differ materially at two such points, each in the region whereR/L is small, if between them the particle traverses a region whereR/L is not small. This region of non-adiabatic motion ‘scatters’ the pitch angles.

The magnetic structure of Co 3O 4

The paper reports theoretical evidence that the multi-spin-axis magnetic structure proposed in 1964 by van Laar actually does exist in CoO. This tetragonal spin arrangement produces both the strong tetragonal and the weaker monoclinic distortion experimentally observed in this material. The tetragonal distortion is a product of the magnetostriction and dislocations of the Co atoms necessary for the magnetic state to be an eigenstate of the system and causes in turn a monoclinic-like distortion of the array of the oxygen atoms comparable with the rombohedral-like distortion of the oxygen atoms recently proposed to be present in NiO and MnO. The monoclinic-like distortion has no influence on the tetragonal magnetic structure which is generated by a special nonadiabatic atomic-like motion of the electrons near the Fermi level qualifying, in addition, CoO to be a Mott insulator.

An Example of the Non-Adiabatic Motion of a Charged Particle in an External Magnetic Field

Two particles of the same charge and with nearly equal initial momentums are shown to drift in opposite directions in certain magnetic fields varying steeply over a distance of the order of the cyclotron radius. (auth)

On the spherically symmetric non-adiabatic motion of a gas sphere

view Abstract Citations (1) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the spherically symmetric non-adiabatic motion of a gas sphere McVittie, G. C. ; Rogers, M. H. Abstract . Exact solutions of the equations of classical gas dynamics are used to describe an idealized model of a supernova explosion. The total loss of energy is evaluated in terms of the intial central temperature and the mass concentration of the star, and it is found that each for value of the mass concentration there is a unique central temperature below which no energy can be emitted. A central temperature of twenty million degrees is then assumed and the amounts of energy emitted for varying values of the mass concentration are calculated; these are found to be of the order of I0 ergs. Publication: The Astronomical Journal Pub Date: November 1955 DOI: 10.1086/107241 Bibcode: 1955AJ.....60..374M full text sources ADS |