Theory of 2D plasma waves as a sensitive probe of nonlinear effects due to compressibility of 4He

Putterman, Seth; Roberts, Paul; Fiszdon, W.

doi:10.1016/0375-9601(88)90910-3

Cited by 6 publications

(5 citation statements)

References 7 publications

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“…Veit Elser and P. M. Platzman AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (Received 11 March 1988) We propose a simple mechanism that generates nonparabolicity in the dispersion of the positive charge carrier (snowball) in superfluid 4 He. Specifically, we pursue the consequences of a model where (1) the snowball behaves as a rigid rotator and (2) the hydrodynamic contribution to its mass (with rotator axes fixed) is anisotropic.…”

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

“…PACS numbers: 67.40.Yv Recent measurements at millikelvin temperatures ' indicate a substantial linear variation in the effective mass of the positve charge carrier (ion) in superfluid 4 He. As in the earlier experiment at somewhat higher temperatures by Ott-Rowland et al, 3 the effective ion mass is inferred from resonant modes of pools of ions trapped below the liquid surface.…”

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

“…The structure of the positive ion in 4 He has been qualitatively described by the "snowball" model. 5 " 7 The helium atoms in the core of the ion are believed to form a solid by virtue of the strong electrostrictive attraction to the positive charge.…”

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

“…This number corresponds to one atom or a tightly bound dimer or trimer at the center surrounded by a single shell of atoms. In light of this we view the positve ion in 4 He as a small and not necessarily spherical cluster.…”

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

“…These energies are still smaller by a factor of 25-100 than the excitation energies implicit in a calculation of nonparabolicity generated by compression. 4 Compression may be understood as the mixing of the superfluid "vacuum" with the one-phonon state. The relevant phonons will have wavelengths comparable to the snowball dimension and consequently energies on the order of 10 K. The superflow assumption which underlies the first two terms in (1) is valid as long as the rotator axis n is fixed and the ion velocity, pi Mb, does not exceed the critical velocity for roton creation.…”

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

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Spinning "Snowballs" in SuperfluidHe4

Elser

Platzman

1988

Phys. Rev. Lett.

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We propose a simple mechanism that generates nonparabolicity in the dispersion of the positive charge carrier (snowball) in superfluid 4 He. Specifically, we pursue the consequences of a model where (1) the snowball behaves as a rigid rotator and (2) the hydrodynamic contribution to its mass (with rotator axes fixed) is anisotropic. The nonparabolicity that we calculate leads to a linear temperature variation of the snowball effective mass. The model is consistent with recent measurements if we assume a mass anisotropy of (9-13)%. An additional T 3 mass enhancement by long-wavelength phonons is negligible for the snowball but may be observable for the negative charge carrier.PACS numbers: 67.40.Yv Recent measurements at millikelvin temperatures ' indicate a substantial linear variation in the effective mass of the positve charge carrier (ion) in superfluid 4 He. As in the earlier experiment at somewhat higher temperatures by Ott-Rowland et al., 3 the effective ion mass is inferred from resonant modes of pools of ions trapped below the liquid surface. In this Letter we consider a source of nonparabolicity in the dispersion of the positive ion. In close analogy to the case of elastic constants in anharmonic solids, nonparabolicity in the dispersion then leads to a temperature-dependent mass. Putterman, Roberts, and Fiszdon 4 have evaluated the strength of the nonparabolicity arising from compression of the liquid surrounding the ion and find that it is too small by about a factor of 350 to explain the observations. We propose a much stronger source of nonparabolicity that results from the rotational degree of freedom and associated mass anisotropy of the positive ion. When compared with experiment our results provide interesting information about the structure of this ion. We also suggest new experiments to spectroscopically probe its rotational modes.The ion-pool experiments have utilized two independent probes of the positive-ion effective mass: (1) the absolute value of the plasma frequency 1,2 and (2) the cyclotron shift of the plasma frequency. * Consistency in the temperature variation of the ion effective mass as inferred from (1) and (2) suggests that an intrinsic property of the ion is being measured rather than a collective phenomenon. Indeed, the strong nonlinear response observed by (backbending of the resonance curve) is attributed by Putterman, Roberts, and Fiszdon 4 to the same nonparabolicity responsible for the mass variation rather than the much weaker pondermotive nonlinearity in the plasma equations. Finally, the cyclotron frequency shifts were shown to be independent of trapping depth 1 so that surface effects (e.g., ripplons) evidently also play no significant role.The structure of the positive ion in 4 He has been qualitatively described by the "snowball" model. 5 " 7 The helium atoms in the core of the ion are believed to form a solid by virtue of the strong electrostrictive attraction to the positive charge. The size of the solid core can be estimated by the location of the distance from t...

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Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

Section: Spinning "Snowballs" In Superfluid 4 Hementioning

confidence: 99%

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Spinning "Snowballs" in SuperfluidHe4

Elser

Platzman

1988

Phys. Rev. Lett.

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Ions trapped below the surface of superfluid helium. I. The observation of plasma resonances, and the measurement of effective masses and ionic mobilities

Barenghi

Mellor

Meredith

et al. 1991

Phil. Trans. R. Soc. Lond. A

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The results are reported of experiments on two-dimensional pools of positive and negative ions trapped below the surface of superfluid 4 He. The results of detailed computations on the static characteristics of an ion pool are presented, from which it is possible to deduce the size of the pool from the known potentials applied to the surrounding electrodes and the measured total charge in the pool. At the higher tem peratures, between 1 K and about 300 mK, the ionic mobility can be obtained from measurements of the non-resonant response of the ions in the pool with a capacitance-conductance bridge connected to a pair of the surrounding electrodes; the theory underlying this technique is described in detail, and experimental results are presented. At lower tem peratures sharp plasm a resonances can be excited, and detailed studies of these resonances have been made in the temperature range from 25 mK to 130 mK for negative ions and from 15 mK to 450 mK for positive ions. Ionic effective masses have been deduced from the observed resonant frequencies, but the resulting values are in some respects unreliable for reasons that are explained. Ionic mobilities have been deduced from the observed damping of the plasma resonances; they are compared with the results of earlier experiments at higher temperatures, but the comparison with theory will be presented in a separate paper. The ion pools have been cooled on many occasions below the temperature at which there is a transition to a Wigner crystal, but no corresponding change has been observed in the behaviour of the mobility or of the plasma resonances.

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Two-dimensional ion-plasma resonances under the surface of liquid helium

Hannahs

Williams

1990

Phys. Rev. B

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Theory of 2D plasma waves as a sensitive probe of nonlinear effects due to compressibility of 4He

Cited by 6 publications

References 7 publications

Spinning "Snowballs" in SuperfluidHe4

Spinning "Snowballs" in SuperfluidHe4

Ions trapped below the surface of superfluid helium. I. The observation of plasma resonances, and the measurement of effective masses and ionic mobilities

Two-dimensional ion-plasma resonances under the surface of liquid helium

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