Equilibrium theory of cylindrical discharges with special application to helicons

Radiofrequency discharges used in industry often have centrally peaked plasma density profiles n(r) although ionization is localized at the edge, even in the presence of a dc magnetic field. This can be explained with a simple cylindrical model in one dimension as long as the short-circuit effect at the endplates causes a Maxwellian electron distribution. Surprisingly, a universal profile can be obtained, which is self-similar for all discharges with uniform electron temperature Te and neutral density nn. When all collisions and ionizations are radially accounted for, the ion drift velocity toward the wall reaches the Bohm velocity at a radius which can be identified with the sheath edge, thus obviating a pre-sheath calculation. For non-uniform Te and nn, the profiles change slightly but are always peaked on axis. For helicon discharges, iteration with the HELIC code for antenna-wave coupling yields profiles consistent with both energy deposition and diffusion profiles. Calculated density is in absolute-v...

[1]  A. Fruchtman.  Nonmonotonic plasma density profile due to neutral-gas depletion , 2010 .

[2]  Francis F. Chen.  Electrostatic stability of a collisionless plane discharge , 1962 .

[3]  A. Fruchtman.  Ambipolar and nonambipolar cross-field diffusions , 2009 .

[4]  H. Torreblanca,et al.  Density jump in helicon discharges , 2007 .

[5]  W. Dorland,et al.  Plasma Physics and Controlled Fusion , 1984 .

[6]  G. Tynan,et al.  Measurement of radial neutral pressure and plasma density profiles in various plasma conditions in large-area high-density plasma sources , 2000 .

[7]  A. Lichtenberg,et al.  Principles of Plasma Discharges and Materials Processing , 1994 .

[8]  Valery Godyak,et al.  Soviet radio frequency discharge research , 1986 .

[9]  Konstantin P. Shamrai,et al.  Volume and surface rf power absorption in a helicon plasma source , 1996 .

[10]  Hajime Sugai,et al.  Low-temperature Plasmas, Plasma Applications, Plasma Sources, Sheaths The role of Trivelpiece-Gould waves in antenna coupling to helicon waves , 2000 .

[11]  A. Simon.  Ambipolar Diffusion in a Magnetic Field , 1955 .

[12]  Suwon Cho,et al.  The field and power absorption profiles in helicon plasma resonators , 1996 .

[13]  G. Borg,et al.  A 1D cylindrical kinetic wave code for helicon plasma sources , 1998 .

[14]  V. Vahedi.  Modeling and Simulation of RF Discharges Used for Plasma Processing. , 1993 .

[15]  J. J. Thomson,et al.  Conduction of electricity through gases , 1903 .

[16]  I. Langmuir.  The Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths , 1929 .

[17]  J. Scharer,et al.  Wave propagation and absorption simulations for helicon sources , 1998 .

[18]  A. W. Trivelpiece,et al.  Space Charge Waves in Cylindrical Plasma Columns , 1959 .

[19]  R. H. Fowler.  The Mathematical Theory of Non-Uniform Gases , 1939, Nature.

[20]  M. Meyyappan,et al.  Modeling of a helicon plasma source , 2003 .

[21]  J. Allen,et al.  Coaxial discharge with axial magnetic field: Demonstration that the Boltzmann relation for electrons generally does not hold in magnetized plasmas , 2010 .

[22]  R. S. Robinson.  Energetic binary collisions in rare gas plasmas , 1979 .

[23]  P. Chabert,et al.  Enhanced plasma transport due to neutral depletion. , 2005, Physical review letters.

[24]  E. Harrison,et al.  The Low Pressure Plane Symmetric Discharge , 1959 .

[25]  R. Boswell,et al.  Plasma production using a standing helicon wave , 1970 .

[26]  M. Krämer,et al.  Excitation of short-scale fluctuations by parametric decay of helicon waves into ion–sound and Trivelpiece–Gould waves , 2005 .

[27]  V. Rozhansky,et al.  Fast expansion of a plasma beam controlled by short-circuiting effects in a longitudinal magnetic field , 1996 .

[28]  A. Aanesland,et al.  Direct measurements of neutral density depletion by two-photon absorption laser-induced fluorescence spectroscopy , 2007 .

[29]  K. Riemann,et al.  The influence of collisions on the plasma sheath transition , 1997 .

[30]  A. Lichtenberg,et al.  Principles of Plasma Discharges and Materials Processing: Lieberman/Plasma 2e , 2005 .

[31]  R. Landshoff,et al.  Introduction to the Theory of Ionized Gases , 1961 .

[32]  J. Delcroix,et al.  Théorie cinétique des plasmas homogènes faiblement ionisés - III. L'opérateur de collision dans le cas du gaz de Lorentz imparfait , 1956 .

[33]  A. Fruchtman,et al.  Two-dimensional equilibrium of a low temperature magnetized plasma , 2005 .

[34]  A. Phelps,et al.  Collision cross sections for argon atoms with argon atoms for energies from 0.01 eV to 10 keV , 2000 .

[35]  N. Sternberg,et al.  Magnetic field effects on gas discharge plasmas , 2006 .

[36]  D. Rapp,et al.  CHARGE EXCHANGE BETWEEN GASEOUS IONS AND ATOMS. , 1962 .

[37]  F.F. Chen.  Nonlinear effects and anomalous transport in RF plasmas , 2006, IEEE Transactions on Plasma Science.

[38]  L. M. Biberman,et al.  Kinetics of Nonequilibrium Low-Temperature Plasmas , 1987 .

[39]  J. Evans,et al.  Nonlocal power deposition in inductively coupled plasmas. , 2001, Physical review letters.

[40]  M. A. Biondi,et al.  Mobilities of Atomic and Molecular Ions in the Noble Gases , 1954 .

[41]  James F. Allen.  The Plasma Boundary in a Magnetic Field , 2008 .

[42]  R. K. Wakerling,et al.  The characteristics of electrical discharges in magnetic fields , 1949 .

[43]  L. Holland.  Plasma Phenomena in Gas Discharges , 1977 .

[44]  F. Witteborn,et al.  Measurements of resonant charge exchange cross sections in nitrogen and argon between 0.5 and 17 eV , 1966 .

[45]  Michael A. Lieberman,et al.  Self-consistent discharge characteristics of collisional helicon plasmas , 2003 .

[46]  Sanborn C. Brown,et al.  Basic Data of Plasma Physics , 1961 .

[47]  Benjamin Alexandrovich,et al.  Electron energy distribution function measurements and plasma parameters in inductively coupled argon plasma , 2002 .

[48]  F. S.,et al.  Conduction of Electricity through Gases , 1903, Nature.