A Hamiltonian formalism for studying the dynamics of a dust particle with variable electric charge in dusty plasma is proposed. The Hamiltonian and the equations of motion are presented and the dynamics is shown to be conservative. The problem is cast in terms of the motion of a particle with a constant fictitious chargeAQ moving in a suitably defined potential, while the actual particle charge is spatially distributed. With this formalism, the problem of trapping of dust particles in potential wells and barriers is studied. The results show that because of the spatial “delocalization”/distribution of the particle charge, a particle with insufficient energy to cross the potential barrier can penetrate it to tunnel out i.e., “classical tunnelling”; similar to a high jumper clearing the bar by the Fosbury flop technique or the usual quantum tunnelling. For energies greater than a critical value, the charged particle is shown to tunnel out of even an infinitely deep potential well. A modified criterion for trapping in potential wells is given.
About the Speaker
Prof Avinash Khare did PhD from PRL in 1984 in the field of Mirror Machines. Subsequently he joined PPP and later IPR where he remained until 2000. Since 2005 he is in the department of Physics and Astrophysics, University of Delhi. Currently he is the Vice Chancellor of Sikkim Central University, Gangtok, Sikkim. In between he was at JET ad Culham Lab 1986- 1989, University of California 1995, Univesity of Iowa 2001-2003, Univ. of Columbia 2004-2005 and a research professor at University of Alabama at Huntsville since 2010. Professor Khare’s major contributions include a theory of ideal internal kink in tokamak which he proposed with J. B. Taylor, Steven Cowley and Jim Hastie. In field of dusty plasmas he has proposed a theory of critical point and phase coexistence and predicted the existence of electrostatic pressure which has been verified experimentally. In non neutral plasma he did early work on toroidal equilibrium and confinement. In space physics he has predicted the existence of compact dust objects. Along with Russian mathematician Academician V. L. Rvachev he has proposed Non Archimedean algebra, which is the mathematics of numbers without infinity and applied it to cosmology, gravitation and computers. He has also proposed and patented dust plasma thruster which is novel space propulsion techniques and a new type of heat pump and engine which works using electric fields.
Prof Khare served as vice president (2000-02) and president (2010-12) of PSSI. He is a fellow of all three major academies i.e., Indian National Science Academy Delhi. National Academy of Sciences (India), Allahabad and Indian Academy of Sciences, Bengaluru. He is also a recipient of Homi Bhabha Fellowship Award (1993-95). He has recently been awarded Biren Roy Memorial medal of Indian National Science Academy.