Information hidden in the velocity distribution of ions and the exact kinetic Bohm criterion

Non-equilibrium distribution functions of electrons and ions play an important role in plasma physics. A prominent example is the kinetic Bohm criterion. Since its first introduction it has been controversial for theoretical reasons and due to the lack of experimental data, in particular on the ion distribution function. Here we resolve the theoretical as well as the experimental difficulties by an exact solution of the kinetic Boltzmann equation including charge exchange collisions and ionization. This also allows for the first time non-invasive measurement of spatially resolved ion velocity distributions, absolute values of the ion and electron densities, temperatures, and mean energies as well as the electric field and the plasma potential in the entire plasma. The non-invasive access to the spatially resolved distribution functions of electrons and ions is applied to the problem of the kinetic Bohm criterion. Theoretically a so far missing term in the criterion is derived and shown to be of key importance. With the new term the validity of the kinetic criterion at high collisionality and its agreement with the fluid picture are restored. All findings are supported by experimental data, theory and a numerical model with excellent agreement throughout.

[1]  M. Benilov.  Comment on ‘Information hidden in the velocity distribution of ions and the exact kinetic Bohm criterion’ , 2019, Plasma Sources Science and Technology.

[2]  N. Timofeev,et al.  Comment on ‘Information hidden in the velocity distribution of ions and the exact kinetic Bohm criterion’ , 2018 .

[3]  U. Czarnetzki,et al.  Ignition and afterglow dynamics of a high pressure nanosecond pulsed helium micro-discharge: I. Electron, Rydberg molecules and He (23S) densities , 2016 .

[4]  U. Czarnetzki,et al.  The exact form of the Bohm criterion for a collisional plasma , 2016, 1603.00515.

[5]  Francis F. Chen,et al.  Introduction to Plasma Physics and Controlled Fusion , 2015 .

[6]  U. Czarnetzki,et al.  Comment on: Measurement of the force exerted on the surface of an object immersed in a plasma , 2015 .

[7]  D. Tskhakaya,et al.  Unified Bohm criterion , 2015 .

[8]  V. Godyak,et al.  Langmuir paradox revisited , 2015 .

[9]  H. Valentini,et al.  The limits of the Bohm criterion in collisional plasmas , 2015 .

[10]  S. Daniels,et al.  A spatially resolved retarding field energy analyzer design suitable for uniformity analysis across the surface of a semiconductor wafer. , 2014, The Review of scientific instruments.

[11]  U. Czarnetzki.  Analytical model for the radio-frequency sheath. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  S. Robertson.  Sheaths in laboratory and space plasmas , 2013 .

[13]  W. Jacob,et al.  Quantitative determination of mass-resolved ion densities in H2-Ar inductively coupled radio frequency plasmas , 2013 .

[14]  K. Riemann.  Comment on ‘Kinetic theory of the presheath and the Bohm criterion’ , 2012 .

[15]  C. Cardinaud,et al.  Ion energy distributions measured inside a high-voltage cathode in a BF3 pulsed dc plasma used for plasma doping: experiments and ab initio calculations , 2012 .

[16]  Jm Jose Palomares,et al.  Experimental investigation of the electron energy distribution function (EEDF) by Thomson scattering and optical emission spectroscopy , 2012 .

[17]  M. Benilov,et al.  Physics of the intermediate layer between a plasma and a collisionless sheath and mathematical meaning of the Bohm criterion , 2012 .

[18]  U. Czarnetzki,et al.  Recombination and enhanced metastable repopulation in the argon afterglow. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  U. Czarnetzki,et al.  Electron cooling in decaying low-pressure plasmas. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  N. Hershkowitz,et al.  Comment on "Ar+ and Xe+ velocities near the presheath-sheath boundary in an Ar/Xe discharge". , 2012, Physical review letters.

[21]  Å. Fredriksen,et al.  Ion velocity distributions in the sheath and presheath of a biased object in plasma , 2011 .

[22]  M. Lieberman,et al.  Ar+ and Xe+ velocities near the presheath-sheath boundary in an Ar/Xe discharge. , 2011, Physical review letters.

[23]  U. Czarnetzki,et al.  Determination of electron densities by diode-laser absorption spectroscopy in a pulsed ICP , 2011 .

[24]  C. Hegna,et al.  Reply to comment on ‘Kinetic theory of the presheath and the Bohm criterion’ , 2010, 1212.4226.

[25]  N. Hershkowitz,et al.  Experimental Test of Instability-Enhanced Collisional Friction for Determining Ion Loss in Two Ion Species Plasmas , 2010 .

[26]  U. Czarnetzki,et al.  Argon ion velocity distributions in a helicon discharge measured by laser induced fluorescence , 2010 .

[27]  C. Hegna,et al.  Instability-enhanced collisional friction can determine the Bohm criterion in multiple-ion-species plasmas. , 2009, Physical review letters.

[28]  J. Allen.  The plasma–sheath boundary: its history and Langmuir's definition of the sheath edge , 2009 .

[29]  T. Tsankov,et al.  Two-dimensional fluid model of a two-chamber plasma source , 2008 .

[30]  T. Lunt,et al.  Experimental investigation of the plasma-wall transition. , 2008, Physical review letters.

[31]  U. Czarnetzki,et al.  Phase resolved measurement of anisotropic electron velocity distribution functions in a radio-frequency discharge , 2008 .

[32]  B. Smirnov.  Plasma Processes and Plasma Kinetics , 2007 .

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

[34]  U. Czarnetzki,et al.  Plasma diagnostics by laser spectroscopic electric field measurement , 2005 .

[35]  Z. Sternovsky.  The effect of ion–neutral collisions on the weakly collisional plasma-sheath and the reduction of the ion flux to the wall , 2005 .

[36]  Subrata Roy,et al.  Modeling low pressure collisional plasma sheath with space-charge effect , 2003 .

[37]  N. Hershkowitz,et al.  Experimental studies of the Bohm criterion in a two-ion-species plasma using laser-induced fluorescence. , 2003, Physical review letters.

[38]  R. Wendt,et al.  Interpretation of ion distribution functions measured by a combined energy and mass analyzer , 2003 .

[39]  S. Vrhovac,et al.  Momentum transfer theory of ion transport under the influence of resonant charge transfer collisions: the case of argon and neon ions in parent gases , 2002 .

[40]  N. Hershkowitz,et al.  First experimental measurements of the plasma potential throughout the presheath and sheath at a boundary in a weakly collisional plasma. , 2002, Physical review letters.

[41]  R. Franklin.  What significance does the Bohm criterion have in an active collisional plasma-sheath? , 2002 .

[42]  I. Kaganovich.  How to patch active plasma and collisionless sheath: A practical guide , 2002, physics/0208041.

[43]  U. Czarnetzki,et al.  Investigations on ionic processes and dynamics in the sheath region of helium and hydrogen discharges by laser spectroscopic electric field measurements , 2001 .

[44]  U. Czarnetzki,et al.  Space and time resolved electric field measurements in helium and hydrogen RF-discharges , 1999 .

[45]  E. Tatarova,et al.  Noise reduction in EEDF numerical differentiation technique , 1998 .

[46]  X. Chen.  Sheath criterion and boundary conditions for an electrostatic sheath , 1998 .

[47]  K. Riemann.  The Bohm criterion and boundary conditions for a multicomponent system , 1995 .

[48]  F. Doveil,et al.  Ion velocity distribution function observations in a multipolar argon discharge , 1995 .

[49]  Kortshagen.  Experimental evidence on the nonlocality of the electron distribution function. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[50]  R. J. Brunt,et al.  Kinetic‐energy distributions of ions sampled from argon plasmas in a parallel‐plate, radio‐frequency reference cell , 1994 .

[51]  Benjamin Alexandrovich,et al.  Measurement of electron energy distribution in low-pressure RF discharges , 1992 .

[52]  J. Goree,et al.  Laser-induced fluorescence characterization of a multidipole filament plasma , 1991 .

[53]  Hamaguchi,et al.  Ion distribution function in a weakly collisional sheath. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[54]  K. Riemann,et al.  The Bohm criterion and sheath formation , 1991 .

[55]  Valery Godyak,et al.  Smooth plasma-sheath transition in a hydrodynamic model , 1990 .

[56]  Lawler Je.  Equilibration distance of ions in the cathode fall , 1985 .

[57]  K. Riemann,et al.  Kinetic theory of the plasma sheath transition in a weakly ionized plasma , 1981 .

[58]  W. D. Davis,et al.  Ion Energies at the Cathode of a Glow Discharge , 1963 .

[59]  R. Boyd,et al.  The operation of Langmuir probes in electro-negative plasmas , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

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