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2 results

  • 10 - From Black Holes to Random Forces

  • from Part II
  • T. M. Helliwell, Harvey Mudd College, California, V. V. Sahakian, Harvey Mudd College, California
  • Book:
    Modern Classical Mechanics
    Published online:
    30 November 2020
    Print publication:
    10 December 2020, pp 395-434

  • Summary

    In this second capstone chapter, we extend some of the classical mechanics from the preceding four chapters into the context of more recent developments in physics. We begin with gravitation, including some of the ideas that led Einstein to go way beyond Newton’s nonrelativistic theory to find a fully relativistic theory of gravitation. After years of strenuous effort, his work finally culminated in his stunningly original and greatest single achievement, the general theory of relativity. He was able to predict three effects that could be measured in the solar system, which he used to check his theory. We will cover all three of these. Then we will introduce so-called “magnetic gravity,” which contains the leading terms in general relativity in a form much like Maxwell’s equations for electromagnetism. Next, we delve just a bit deeper into gauge symmetry in Maxwell’s theory, partly because it deepens our understanding of electromagnetism but also because gauge symmetry has played such a large role in physical theories over the past many decades. Finally, we introduce stochastic forces, which are not fundamental forces but the result of huge numbers of small collisions.

  • Anomalous skin effect for linearly and circularly polarized intense laser light

  • TATSUFUMI NAKAMURA, SUSUMU KATO, TOMOKAZU KATO
  • Journal:
    Laser and Particle Beams / Volume 20 / Issue 1 / January 2002
    Published online by Cambridge University Press:
    05 August 2002, pp. 101-107

  • Anomalous absorption of an intense short laser pulse in overdense plasmas is analyzed with a stochastic theory. A diffusion equation describing a time evolution of the electron distribution function is derived. From the equation it is shown that the electron distribution function becomes anisotropic in the momentum space, which gives rise to the absorption of the energy. The diffusion is not dominant in the pz direction, which is longitudinal to the vacuum-plasma boundary, rather it is dominant in the px direction, which is transverse to the boundary. However, the diffusion in pz enhances the absorption. Analytical expressions of the absorption coefficient and skin depth are obtained for the anomalous skin effect regime (ω02c2 << ωp2ve2), which evolves in time as the electron distribution becomes anisotropic. The asymptotic value of the absorption coefficient is proportional to [square root]I. The temperature and density dependence of the absorption coefficient is also discussed.