*Helmut Hofmann*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0016
- Subject:
- Physics, Nuclear and Plasma Physics

The stability of metal clusters exhibits shell effects similar to that of nuclei. This chapter reviews how this feature is treated in the jellium model. The main focus is on optical properties ...
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The stability of metal clusters exhibits shell effects similar to that of nuclei. This chapter reviews how this feature is treated in the jellium model. The main focus is on optical properties described by the dielectric function, which is analyzed in greater detail, first for the Drude-Lorentz model then for a fully quantal treatment. With increasing volume of the clusters, only bulk properties typical for a metal are important. For smaller systems, quantum size effects come into play. This effect is studied, reporting on microscopic calculations within the jellium model. Of special interest is the damping width, for which finite values are obtained even at small frequencies if the quantal electronic states are treated as being quasi-continuous. This mechanism is often associated with Landau damping known to conserve entropy. The problem related to this fact is examined, together with the analogous one of wall friction in finite nuclei.Less

The stability of metal clusters exhibits shell effects similar to that of nuclei. This chapter reviews how this feature is treated in the jellium model. The main focus is on optical properties described by the dielectric function, which is analyzed in greater detail, first for the Drude-Lorentz model then for a fully quantal treatment. With increasing volume of the clusters, only bulk properties typical for a metal are important. For smaller systems, quantum size effects come into play. This effect is studied, reporting on microscopic calculations within the jellium model. Of special interest is the damping width, for which finite values are obtained even at small frequencies if the quantal electronic states are treated as being quasi-continuous. This mechanism is often associated with Landau damping known to conserve entropy. The problem related to this fact is examined, together with the analogous one of wall friction in finite nuclei.

*Olle Eriksson, Anders Bergman, Lars Bergqvist, and Johan Hellsvik*

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788669
- eISBN:
- 9780191830747
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788669.003.0009
- Subject:
- Physics, Atomic, Laser, and Optical Physics

In this chapter we give several examples of how the multiscale approach for atomistic spin-dynamics, as described in Part I and Part II of this book, performs for describing magnon excitations of ...
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In this chapter we give several examples of how the multiscale approach for atomistic spin-dynamics, as described in Part I and Part II of this book, performs for describing magnon excitations of solids. Due to the recent experimental advancements in detecting such excitations for surfaces and multilayers, we focus here primarily on spin wave excitations of two-dimensional systems. The discussion can easily be generalized to bulk magnets, and in fact some examples of bulk properties are given in this chapter as well. Magnons can be categorized as dipolar and exchange magnons, where the latter are in the range of giga Hz frequency, and are the main focus of this chapter.Less

In this chapter we give several examples of how the multiscale approach for atomistic spin-dynamics, as described in Part I and Part II of this book, performs for describing magnon excitations of solids. Due to the recent experimental advancements in detecting such excitations for surfaces and multilayers, we focus here primarily on spin wave excitations of two-dimensional systems. The discussion can easily be generalized to bulk magnets, and in fact some examples of bulk properties are given in this chapter as well. Magnons can be categorized as dipolar and exchange magnons, where the latter are in the range of giga Hz frequency, and are the main focus of this chapter.

*E. J. N. Wilson*

- Published in print:
- 2001
- Published Online:
- January 2010
- ISBN:
- 9780198508298
- eISBN:
- 9780191706363
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508298.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter shows how multipole magnets generate field shapes corresponding to the terms of a Taylor Series expansion about the centre line of the magnet. Sextupoles produce a parabolic field shape ...
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This chapter shows how multipole magnets generate field shapes corresponding to the terms of a Taylor Series expansion about the centre line of the magnet. Sextupoles produce a parabolic field shape in the median plane, octupoles a cubic, etc. Each term in the expansion drives dangerous lines in the working diagram. An example is the four, third order, resonance lines that converge on points in the working diagram at one third integer values of Q. The effects of these resonances are derived with the help of the circle diagram introduced in Chapter 6. The effect of an n-th order resonance is to produce n islands in phase space, and beyond these, an unstable non-linear growth in amplitude that causes the beam to be lost. Multipoles can however be used to positive effect by introducing a Q that depends on amplitude, contributing to Landau damping of beam instabilities.Less

This chapter shows how multipole magnets generate field shapes corresponding to the terms of a Taylor Series expansion about the centre line of the magnet. Sextupoles produce a parabolic field shape in the median plane, octupoles a cubic, etc. Each term in the expansion drives dangerous lines in the working diagram. An example is the four, third order, resonance lines that converge on points in the working diagram at one third integer values of *Q*. The effects of these resonances are derived with the help of the circle diagram introduced in Chapter 6. The effect of an n-th order resonance is to produce *n* islands in phase space, and beyond these, an unstable non-linear growth in amplitude that causes the beam to be lost. Multipoles can however be used to positive effect by introducing a *Q* that depends on amplitude, contributing to Landau damping of beam instabilities.

*A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo*

- Published in print:
- 2014
- Published Online:
- October 2014
- ISBN:
- 9780199581931
- eISBN:
- 9780191787140
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199581931.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this Chapter a short introduction to the physics of hot plasma is given. The concepts of Debye shielding and quasi-neutrality are in particular discussed. The Vlasov-Maxwell equations are derived ...
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In this Chapter a short introduction to the physics of hot plasma is given. The concepts of Debye shielding and quasi-neutrality are in particular discussed. The Vlasov-Maxwell equations are derived following the Klimontovich approach. Working within the collisionless Vlasov picture, the case of electrostatic waves is presented and the phenomenon of linear Landau damping reviewed in some details. The non linear regime of the wave-particles interaction is also briefly analyzed. Explicit reference is made to the collective BGK and Case-van Kampen modes.Less

In this Chapter a short introduction to the physics of hot plasma is given. The concepts of Debye shielding and quasi-neutrality are in particular discussed. The Vlasov-Maxwell equations are derived following the Klimontovich approach. Working within the collisionless Vlasov picture, the case of electrostatic waves is presented and the phenomenon of linear Landau damping reviewed in some details. The non linear regime of the wave-particles interaction is also briefly analyzed. Explicit reference is made to the collective BGK and Case-van Kampen modes.