Note on ` Non-Linear Hydromagnetic Waves Propagating along a Magnetic Field in a Cold Collision-Free Plasma '

1968 ◽  
Vol 24 (3) ◽  
pp. 660-660 ◽  
Author(s):  
Tsunehiko Kakutani
Keyword(s):  
Magnetic Field ◽  
Non Linear ◽  
Hydromagnetic Waves ◽  
Cold Collision ◽  
Free Plasma

scholarly journals Propagation of a solitary wave along a magnetic field in a cold collision-free plasma

1961 ◽  
Vol 11 (1) ◽  
pp. 16-20 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Magnetic Field ◽  
Geometric Mean ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Order Of Magnitude ◽  
Hydromagnetic Waves ◽  
Cold Collision ◽  
The Magnetic Field ◽  
Free Plasma ◽  
Alfven Velocity

It is shown that solitary hydromagnetic waves can propagate parallel to a uniform magnetic field in a cold collision-free plasma. These waves are exact solutions of the non-linear equations of motion except for the quasi-neutral approximation. The velocity of propagation lies in a range of values somewhat larger than the Alfvén velocity, and is of the order of 25 times the Alfvén velocity for hydrogen, the precise value depending upon the strength of the wave. Simple expressions exist for the velocities of the ions and electrons and the magnetic field inside the wave. The lines of force are spirals about the direction of propagation. The waves are symmetrical about their middle. The order of magnitude of their width is the geometric mean of the gyro-radii of the ions and electrons when moving with the Alfvén velocity. The maximum value of the magnetic field can be somewhat larger than the value away from the wave.

A study of the propagation of a solitary wave along the magnetic field in a cold collision-free plasma

2020 ◽  
Vol 27 (4) ◽  
pp. 042102
Author(s):  
Gohar Abbas ◽  
J. E. Allen ◽  
M. Coppins ◽  
L. Simons ◽  
L. James
Keyword(s):  
Magnetic Field ◽  
Solitary Wave ◽  
Cold Collision ◽  
The Magnetic Field ◽  
Free Plasma

scholarly journals The structure of a hydromagnetic front in a cold collision-free plasma

1962 ◽  
Vol 12 (1) ◽  
pp. 81-87 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Magnetic Field ◽  
Characteristic Frequency ◽  
Cold Plasma ◽  
Equations Of Motion ◽  
One Dimensional ◽  
Infinite Extent ◽  
Cold Collision ◽  
The Magnetic Field ◽  
Free Plasma ◽  
A Current

A one-dimensional steady solution of the equations of motion of a cold plasma in a magnetic field is obtained. The plasma is of semi-infinite extent, bounded by a plane interface which separates it from a vacuum or medium at rest. The particles approach from infinity, are reflected at the front, and return to infinity in the opposite direction. At infinity, the magnetic field is parallel and anti-parallel to the plasma streams, and is inclined at an angle to the normal to the interface. The front is a current sheet across which the lines of force are bent, with the component of the magnetic field in the plane of the front changing direction. The inertia of the electrons is neglected, and the characteristic frequency associated with the front is the ion gyro-frequency.

The structure of quasi-shocks in a collision-free plasma in a magnetic field

1967 ◽  
Vol 1 (1) ◽  
pp. 129-144 ◽  
Author(s):  
J. G. Cordey ◽  
P. G. Saffman
Keyword(s):  
Magnetic Field ◽  
Finite Amplitude ◽  
Mean Values ◽  
Turbulent Transition ◽  
Random Manner ◽  
Flow Through ◽  
Steady Solutions ◽  
Flow Variables ◽  
Hydromagnetic Waves ◽  
Free Plasma

A study is made of finite amplitude, oblique, hydromagnetic waves in a cold collision-free plasma. It is shown that the equations admit steady solutions which describe flow through a front. Ahead of the front, the flow is uniform, but behind the front the magnetic field and flow variables oscillate irregularly in a random manner. The fronts are called ‘quasi-shocks’, although they have more in common with the laminar-turbulent transition of fluid mechanics than with the classical shock wave. The structure of the quasi-shocks is examined, and estimates are made for the mean values behind the front. The relevance of the quasishocks to the so-called ‘collision-free shock’ is considered, and comparison is made with the ‘bow shock’ on the solar wind near the earth. It is shown that the quasi-shock is consistent with some of the observed data.

Non-linear dependence of the dielectric properties of chick embryo myoblast membranes exposed to a sinusoidal 50 Hz magnetic field

1991 ◽  
Vol 60 (6) ◽  
pp. 877-890 ◽  
Author(s):  
Martino Grandolfo ◽  
Maria Santini ◽  
Paolo Vecchia ◽  
Adalberto Bonincontro ◽  
Cesare Cametti ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Dielectric Properties ◽  
Chick Embryo ◽  
Linear Dependence ◽  
Non Linear

A shallow-liquid theory in magnetohydrodynamics

1960 ◽  
Vol 7 (1) ◽  
pp. 81-107 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Magnetic Field ◽  
Mechanical Energy ◽  
Fluid Velocity ◽  
Linear Equations ◽  
Qualitative Difference ◽  
Meridional Plane ◽  
Plane Flow ◽  
Non Linear ◽  
Moderate Magnetic Field ◽  
Approximate Equations

The non-linear and linear ‘shallow-water’ theories, which describe long gravity waves on the free surface of an inviscid liquid, are extended to the case of an electrically conducting liquid on a horizontal bottom, in the presence of a vertical magnetic field. The dish holding the liquid, and the medium outside it, are assumed to be non-conducting. The approximate equations are based on a small ratio of depth to wavelength, on the properties of mercury, and on a moderate magnetic field strength. These equations have a ‘magneto-hydraulic’ character, for in the shallow liquid layer the horizontal fluid velocity and current density are independent of the vertical co-ordinate.Some explicit solutions of the linear equations are obtained for plane flows and for axi-symmetric flows in which the velocity vector lies in a vertical, meridional plane. The amplitudes of waves in a dish, and the amplitudes behind wave fronts progressing into undisturbed liquid, are found to be exponentially damped, the mechanical energy associated with a disturbance being dissipated by Joule heating.The approximate non-linear equations for plane flow are studied by means of characteristic variables, and it appears that, because of the magnetic damping effect, there is less qualitative difference between solutions of the non-linear and linear approximate equations at large times than is the case when the magnetic field is absent. In particular, the characteristic curves depart only a finite distance from their ‘undisturbed positions’.

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