Single Particle Motion in Electric and Magnetic Fields (Winter 2011)

Physics 180E
Single Particle Motion in Electric and Magnetic Fields (Winter 2011)

The following photographs were made in the Physics 180E undergraduate laboratory course in plasma physics by Professor Reiner L. Stenzel. They are designed to demonstrate the single particle motion in electric and magnetic fields. A weak electron beam of typically 100 eV, 1-10 mA is injected from an oxide-coated cathode into a low pressure (0.2 mTorr) argon gas. The beam partially ionizes the gas. A second filament is also installed for providing a background plasma. The background plasma has a potential close to that of the grounded chamber wall unless a large (5x6cm) grid is biased positively. The beam electrons are accelerated by an electric field mainly concentrated in the cathode sheath. The trajectory of the beam electrons is visible due to light excitation when the beam electrons collide with argon atoms. No visible light is produced when the electron energy is below typically 10 eV. Several basic phenomena can be inferred from the following pictures.

In these experiments observe carefully, record your observations, think about them whether they fit to basic theories or not, and keep questioning your findings.

See figure caption Fig. 1. View of the cathode for emitting electrons into aa low density background plasma. The electrons are accelerated by an electric field localized in a thin sheath in front of the emissive surface. The heater wire is hidden inside a cold cylinder which avoids a bright light source. The beam is visible because some electrons collide with neutral argon atoms and excite the bound electrons which produces light excitation during the electron relaxation. Some electrons are released from the atoms and form an invisible background plasma.

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See figure caption Fig. 2. A 100 eV electron beam is injected from a BaO coated cathode. The beam spreads. No magnetic field is applied. What does this imply for the equipotential surfaces near the cathode? Is the beam space charge responsible for the spread? Calculate the beam density and the rsadial space charge field in the absence of a background plasma.

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See figure caption Fig. 3. A beam with radial spread is injected along a magnetic field. Explain the shape of the light pattern. What determines the periodic length scale and the maximum radial width?

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See figure caption Fig. 4. A 100 eV beam is injected against a biased grid. What is the bias of the grid? What are the equipotential surfaces which give rise to the flow of electrons around this obstacle? Why is there a shadow in the left middle? Can the effect be interpreted as a shock wave in the electron flow?

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See figure caption Fig. 5. A 100 eV beam is injected from the right side against a biased grid. In the upper picture the beam passes through the grid. In the lower picture it is reflected. Notice the meniscus-shaped equipotential surface in front of the grid. What defines the light boundary?

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See figure caption Fig. 5. When the grid is biased positively it attracts electrons. For a large positive bias the electrons gain energy in the sheath to excite atoms and produce light. It demonstrates the small extent of the sheath. Explain the color change from the sheath boundary toward the electrode.

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See figure caption Fig. 6. A 100eV electron beam is injected across a uniform magnetic field B. What is the field strength and direction if the hot cathode is 7mm in diameter?

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See figure caption Fig. 7. Side view of an electron beam injected across a uniform magnetic field. Explain the reason for its shape.

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See figure caption Fig. 8. A 100eV electron beam is injected across B and passes through a grounded grid. The electrons pass through the openings of the grid. Why is the beam not changed by the sheath of the grid?

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See figure caption Fig. 9. A 100eV electron beam is injected across B and passes through a negatively biased grid. A second electron beam is generated to the right, which has a lower energy due to its brownish color and smaller Larmor radius. Its radius increases when the grid is biased more negatively. Can you explain this effect?

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See figure caption Fig. 10. The 100eV electron beam is reflected when the grid is biased lower than -100V with respect to ground. Does it matter what the plasma potential is with respect to ground?. The reflected beam continues to spiral around a new field line. Why does the beam change color at the reflection point?

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See figure caption Fig. 11. The beam energy and grid bias are chosen such that the beam is reflected both from the bottom and the top of the grid and nearly forms a horizontal figure 8.

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See figure caption Fig. 12. The beam is reflected multiple times from the grid. Although the E-field is not uniform this is essentially an ExB drift around the grid.

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See figure caption Fig. 13. When the grid is biased positively, say to +300V, a luminous ring appears around the grid and perpendicular to the magnetic field. Based on your previous experience with single particle motions explain this phenomenon.

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See figure caption Fig. 14. Hollow cathodes partially confine electrons emitted by a cathode. This enhances the efficiency for ionization. The cathode is placed on the axis of a cylindrical grid which is biased negatively. A dense plasma forms inside the hollow cathode. More pictures below.

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See figure caption Fig. 15. Plasma formations in a hollow cathode. (a) Electrons emitted from the cathode are accelerated toward the grid which is grounded and acts like a transparent anode. No magnetic field is applied. (b) Ditto when a magnetic field is applied. What is the diameter of the plasma column? (c) Side view showing electron focusing. Explain why? (d) Finally, a negative bias is applied to the grid. The electrons are reflected, ionize and form a dense plasma in which single particle motions cannot be seen.

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See figure caption Fig. 15. Electron deflection by a biased cylindrical grid. Electrons are produced in a discharge on the left hand side and confined by a 30 G axial magnetic field. They stream against the biased cylinder. Judging from the display what is the bias voltage? Can you see the 10 eV equipotential surface? Click on the icon to see displays for different bias voltages. Explain what is happening. What would happen if you confine electrons both axially and radially?

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See figure caption Fig. 16. Electron reflections by a negatively biased cylindrical grid in an axial magnetic field. An attempt is made to create "eigenmodes" with an integer numbers of cyclotron orbits around the cylinder, here aboyt three. Can this be done? Notice that the first reflection is incomplete. Why is part of the beam passing through the grid? Ignore the semicircular red filament in the background; it is not biased but has been used earlier to produce a background plasma to help activating the beam cathode.

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See figure caption Fig. 17. Electron reflections by a negatively biased cylindrical grid in an axial magnetic field with about four cyclotron orbits around the cylinder. Can you see a reflected beam inside the cylinder? Explain why it is there?

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See figure caption Fig. 18. Multiple electron reflections by a negatively biased cylindrical grid in an axial magnetic field. Can one confine electrons around the grid? If so how would the beam current close to ground? Is the orbit a classical ExB drift or the result of multiple reflections from the grid sheath?

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See figure caption Fig. 19. Close-up view of the beam reflection process: Notice the beam striations upon reflection and transmission. There are reflected beams outside the region of the incident beam. Explain. Notice that the reflection enhances the beam angular spread. Why? What is the effect of the radial electric field direction? Is there an electric field outside or inside the cylinder? Is the particle energy conserved upon reflection? What is the effective mean free path for momentum change collisions? How would the beam be effected by an array of biased small spheres? Review or Google the physics of "Coulomb collisions". Photo by Hann Mao.

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See figure caption Fig. 20. Students producing a nonuniform magnetic field with strong permanent magnets, one holding a north pole, the other a south pole. No axial field is applied. Photo by Hann Mao.

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See figure caption Fig. 21. Beam injection against an increasing magnetic field. The beam mirrors and its guiding center (axis of the visible reflected beam flux tube) drifts downward. What is the direction of B and grad B? What is the approximate field strength at the mirror point? Why is the mirror region axially spread out? Why is the reflected beam so dark? Is energy not conserved?

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See figure caption Fig. 22. Beam orbit in a nonuniform magnetic field. If the beam orbit were in a plane can you determine B along the beam from the Lorentz force, mdv/dt=-e(vxB)? Note v=dr/dt=const. Suggest how to find the component of B||v. Photo by Hann Mao.

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More to come...