What are helicons?

2. What are helicons? Helicons are partially ionized RF discharges in a magnetic field. They are basically whistler modes confined to a cylinder. They are much different than in free space; they have E-fields. OLD NEW Long cylinder Permanent magnet

3. Helicons pose unending problems • Why does the amplitude oscillate along the cylinder? • Why is a right-helical antenna better than a left one? • What causes the high ionization efficiency? • Why does an endplate near the antenna increase n? • Why is the ion temperature so high? • Why is a half-wavelength antenna better than a full? • Why is the density peaked at the center? Most discharge theorists treat only collision cross sections and ion distribution functions. UCLA

4. The Trivelpiece-Gould mode: edge ionization An electron cyclotron wave near the edge deposits most of the RF energy UCLA

5. Edge ionization should give a hollow profile But density is almost always peaked at center, even in KTe is peaked at the edge. UCLA

6. Previous attempt for an ICP UCLA

7. Let’s take the simplest realistic problem Eliminate all unnecessary features, and not length! Treat a 1D problem in radius r UCLA

8. The problem is how to treat the ends The sheath drop is normally independent of density UCLA

9. Ion diffusion upsets the balance The short-circuit effect “moves” electrons across B. Sheaths change to preserve neutrality. Electrons can now follow the Boltzmann relation. This happens in nanoseconds. UCLA

10. Sheath drops interchange, creating Er UCLA

11. In equilibrium, n is peaked on center Er and diffusion must be outward if axial flow is slow. n(r) is flat in the limit of all ionization at edge. UCLA

12. Three equations in 3 unknowns: v, n, and  Ion equation of motion: Ion equation of continuity: Simplify the collision terms: Use the Boltzmann relation: UCLA

13. Reduce to one dimension in r Eliminate n and  to get an equation for v(r): Non-dimensionalize: This is an ordinary differential equation for all the plasma profiles. UCLA

14. Rescale r to see structure of the equation We had: Rescale r: Finally: k contains the plasma information: UCLA

15. Solutions for uniform pressure and KTe Solutions for three values of k Rescale r so that ra 1 in each case This profile is independent of pressure, size, and magnetic field. It depends on KTe, but is always peaked at the center. UCLA

16. This profile IS modified: • When Te is changed or varies with r • When nn varies with r (neutral depletion, treated later) • When k varies with r But the central peaking remains UCLA

17. Ionization balance restricts KTe for real r Our previous dimensional equation Solved simultaneously UCLA

18. Improved Te – p0 relation Old, radially averaged data: M.A. Lieberman and A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, 2nd ed. (Wiley-Interscience, Hoboken, NJ, 2005). F. F. Chen and J.P. Chang, Principles of Plasma Processing (Kluwer/Plenum, New York, 2002), UCLA

19. The EQM program solves simultaneously: Ion motion Ionization balance Neutral depletion UCLA

20. Last step: iteration with HELIC UCLA

21. Another layer off the onion! UCLA

22. Title UCLA