Charged particles with a velocity component perpendicular to the field will gyrate around a field line in a generally circular or helical orbit and thus sample some of the field lines that are converging to create the field gradient. The radial component of these field lines, coupled with the azimuthal motion of the particle, will result in a force parallel to the field and directed toward the region of smaller field strength.
A more mathematical treatment of the mirror effect describes it as a result of the adiabatic invariance of the magnetic moment. For a given mirror ratio (the maximum field strength divided by the minimum field strength), particles with a pitch angle (angle between the particle velocity and the magnetic field) greater than a critical value will be reflected, those with a smaller pitch angle will escape. In particular,
This result may be surprising because one might intuitively expect that heavier and faster particles, or those with less electric charge, would be harder to reflect, or that a smaller magnetic field would reflect particles less efficiently. However, it must be remembered that the gyroradius ρ = mv/qB in those circumstances is also larger, so that the radial component of the magnetic field seen by the particle is also larger. It is true that the minimum volume and magnetic energy is larger for the case of fast particles and weak fields, but the mirror ratio required remains the same.
In the sixties and seventies, machines using magnetic mirror confinement were considered a viable candidate for producing fusion energy. The concept was eventually largely abandoned because it proved to be impractical to maintain the necessary non-Maxwellian velocity distribution. Collisions scattered the charged particles so that the pitch angle was too small for containment. In addition, velocity space instabilities contributed to the escape of the plasma. (For a modern attempt, see the Polywell inertial electrostatic confinement design by Robert Bussard.)
Magnetic mirrors play an important role in other types of magnetic fusion energy devices such as tokamaks, where the toroidal magnetic field is stronger on the inboard side than on the outboard side. The resulting effects are known as neoclassical.
Magnetic mirrors also occur in nature. Electrons and ions in the magnetosphere, for example, will bounce back and forth between the stronger fields at the poles.
A magnetic bottle is the superposition of two magnetic mirrors. For example, two parallel coils separated by a small distance, carrying the same current in the same direction will produce a magnetic bottle between them. Particles near either end of the bottle experience a magnetic force towards the center of the region; particles with appropriate speeds spiral repeatedly from one end of the region to the other and back. Magnetic bottles can be used to temporarily trap charged particles. This technique is used to confine very hot plasmas with temperatures of the order of 106 K. In a similar way, the earth's non-uniform magnetic field traps charged particles coming from the sun in doughnut shaped regions around the earth called the "Van Allen radiation belts", which were discovered in 1958 using data obtained by instruments aboard the Explorer I satellite.
Wipo Publishes Patent of Goldman Anthony R. for "Magnetic Bottle System and Methods of Use" (American Inventor)
Nov 16, 2012; GENEVA, Nov. 16 -- Publication No. WO/2012/151320 was published on Nov. 8. Title of the invention: "MAGNETIC BOTTLE SYSTEM AND...