Удержание частиц в зеркальной ловушке при наличии столкновений

Fig. 1. A 100 eV electron beam is injected into a neutral gas without applying external electric or magnetic fields. The beam light starts very close to the cathode indicating that the electrons acquire their full energy in a very thin cathode sheath. Thus, the self-produced plasma acts as an anode. The initial beam convergence indicates concave equipotential surfaces near the cathode, presumably due to a radial density gradient. The beam scatters by collisions and beam-plasma instabilities.
Рис.1 Электронный пучок (100 эВ) инжектируется в газовую среду в отсутствии внешних электрических и магнитных полей. Наиболее яркое свечение пучка сконцентрированное вблизи катода  и свидетельствует о том, что электроны приобрели свою полную энергию в тонком катодном слое. Т.о., самоподдерживаемая плазма выполняет роль анода. Схождение пучка свидетельствует  о наличии эквипотенциальных поверхностей вблизи катода, преимущественно обусловленных наличием радиального градиента плотности. Рассеяние пучка обусловлено столкновениями и пучково-плазменными неустойчивостями.
 

Fig. 2. The beam is injected against a negatively biased grid. When the bias voltage is slightly larger than the cathode voltage most of the beam is reflected but a few electrons are transmitted. Note that the equipotential surface near the grid is not plane but convex. This causes an angular spread of the reflected electrons. Electrons in the center of the beam are normal to the sheath and can pass the grid when their energy exceeds the potential energy of the sheath.

Рис.2 Пучок инжектируется в тормозящее электростатическое поле создаваемое отрицательно заряженной сеткой. Когда приложенное к сетке напряжение превышает напряжение катода большая часть электронов пучка отражается от сетки, незначительная часть проникает  за электродное пространство. Следует отметить, что эквипотенциальная поверхность у сетки не является плоской. Это обуславливает угловую расходимость отраженных электронов. Электроны падающие на поверхность отражающей сетки ортогонально и проникают в за электродное пространство когда их энергия превышает потенциал сетки.

Fig. 3. Beam injection against a very negatively biased grid which reflects all electrons. Note dark sheath near grid where the electron energy is decreased below 10 eV. The electrons stagnate in the dark sheath and form a convex equipotential surface. This causes the reflected beam to be highly divergent.

 

Fig. 4. A 100 eV electron beam injected perpendicular to a dc magnetic field. The sense of the cyclotron orbit implies that the magnetic field points into the plane. From the beam energy and the cyclotron radius the field strength can be calculated. Note that the beam light weakens with propagation distance

 

Fig. 5. A low energy beam is injected across a magnetic field as in Fig. 1. The cyclotron radius is decreased. Note the dark gap between the cathode and beam onset. In this sheath region the electrons still have insufficient energy for light excitation.

 

Fig. 6. A low energy beam is injected against a decelerating electric field. As the beam energy falls below 10 eV the light emission stops. The beam and current continue to flow through the dark region.

 

Fig. 7. At high neutral pressures the injected electron beam rapidly spreads. The electron mean free path can be inferred from the beam decay.

 

Fig. 8. Electron motion in crossed electric and magnetic fields. The trajectory is a cycloid, i.e., a superposition of a circular motion and a constant drift to the right. The cyclotron orbit implies a magnetic field direction into the plane and the E×B drift implies that the electric field points downward. From the known beam energy the field strengths can be obtained from cyclotron radius and guiding center drift.

 

Fig. 9. Mirror reflection of a weak electron beam in a nonuniform magnetic field. The beam is injected oblique to the field lines which converge to the right. Due to the adiabatic invariants (energy and magnetic moment) the parallel energy is converted into perpendicular energy at which point the particles reflect. Alternatively, the parallel motion is decelerated by the repelling force of an increasing magnetic field.

 

Fig. 10. Mirror reflection of a stronger electron beam in a magnetic field which converges to the right. Note that the guiding center (axis of spiral) of the reflected beam does not coincide with that of the incident. This is due to the gradient and curvature drift in a nonuniform field.

 

Fig 11. Multiple reflections of an oblique electron beam in a mirror magnetic field. The cyclotron motion is the fastest periodic motion, followed by the slower bounce motion between the mirror points. Gradient and curvature drifts cause a third, slowest rotation azimuthally around the mirror axis. This is the classical charged particle motion in the ionosphere in Earth's magnetic dipole field. Collisions and other scattering processes diffuse the beam.

 

Fig.12. Electron beam injected into a nonuniform magnetic field with a null line. The beam meanders along a magnetic null line pointing diagonally down to the right. Note the reversal of the cyclotron rotation as the magnetic field reverses to either side of the neutral line. Such meandering and figure-eight trajectories have been studied theoretically in the problem of magnetic reconnection occuring in the magnetosphere and on the sun.