# Fast-to-Alfven mode conversion mediated by the Hall current. I. Cold plasma model

Paul Stuart Cally, Elena Khomenko

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

### Abstract

The photospheric temperature minimum in the Sun and solar-like stars is very weakly ionized, with an ionization fraction f as low as 10−4. In galactic star-forming regions, f can be 10−10 or lower. Under these circumstances, the Hall current can couple low-frequency Alfvén and magnetoacoustic waves via the dimensionless Hall parameter $\epsilon =\omega /{{\rm{\Omega }}}_{{\rm{i}}}f,$ where ω is the wave frequency and ${{\rm{\Omega }}}_{{\rm{i}}}$ is the mean ion gyrofrequency. This is analyzed in the context of a cold (zero-β) plasma and in less detail for a warm plasma. It is found that Hall coupling preferentially occurs where the wavevector is nearly field-aligned. In these circumstances, Hall coupling in theory produces a continual oscillation between fast and Alfvén modes as the wave passes through the weakly ionized region. At low frequencies (mHz), characteristic of solar and stellar normal modes, epsilon is probably too small for more than a fraction of one oscillation to occur. On the other hand, the effect may be significant at the far higher frequencies (Hz) associated with magnetic reconnection events. In another context, characteristic parameters for star-forming gas clouds suggest that ${\mathcal{O}}(1)$ or more full oscillations may occur in one cloud crossing. This mechanism is not expected to be effective in sunspots, due to their high ion gyrofrequencies and Alfvén speeds, since the net effect depends inversely on both and therefore inverse quadratically on field strength.
Original language English 1-11 11 The Astrophysical Journal 814 2 https://doi.org/10.1088/0004-637X/814/2/106 Published - 2015

### Keywords

• ISM: clouds
• stars: atmospheres
• Sun: helioseismology
• Sun: oscillations

### Cite this

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title = "Fast-to-Alfven mode conversion mediated by the Hall current. I. Cold plasma model",
abstract = "The photospheric temperature minimum in the Sun and solar-like stars is very weakly ionized, with an ionization fraction f as low as 10−4. In galactic star-forming regions, f can be 10−10 or lower. Under these circumstances, the Hall current can couple low-frequency Alfv{\'e}n and magnetoacoustic waves via the dimensionless Hall parameter $\epsilon =\omega /{{\rm{\Omega }}}_{{\rm{i}}}f,$ where ω is the wave frequency and ${{\rm{\Omega }}}_{{\rm{i}}}$ is the mean ion gyrofrequency. This is analyzed in the context of a cold (zero-β) plasma and in less detail for a warm plasma. It is found that Hall coupling preferentially occurs where the wavevector is nearly field-aligned. In these circumstances, Hall coupling in theory produces a continual oscillation between fast and Alfv{\'e}n modes as the wave passes through the weakly ionized region. At low frequencies (mHz), characteristic of solar and stellar normal modes, epsilon is probably too small for more than a fraction of one oscillation to occur. On the other hand, the effect may be significant at the far higher frequencies (Hz) associated with magnetic reconnection events. In another context, characteristic parameters for star-forming gas clouds suggest that ${\mathcal{O}}(1)$ or more full oscillations may occur in one cloud crossing. This mechanism is not expected to be effective in sunspots, due to their high ion gyrofrequencies and Alfv{\'e}n speeds, since the net effect depends inversely on both and therefore inverse quadratically on field strength.",
keywords = "ISM: clouds, stars: atmospheres, Sun: helioseismology, Sun: oscillations",
author = "Cally, {Paul Stuart} and Elena Khomenko",
year = "2015",
doi = "10.1088/0004-637X/814/2/106",
language = "English",
volume = "814",
pages = "1--11",
journal = "The Astrophysical Journal",
issn = "0004-637X",
publisher = "American Astronomical Society",
number = "2",

}

In: The Astrophysical Journal, Vol. 814, No. 2, 2015, p. 1-11.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Fast-to-Alfven mode conversion mediated by the Hall current. I. Cold plasma model

AU - Cally, Paul Stuart

AU - Khomenko, Elena

PY - 2015

Y1 - 2015

N2 - The photospheric temperature minimum in the Sun and solar-like stars is very weakly ionized, with an ionization fraction f as low as 10−4. In galactic star-forming regions, f can be 10−10 or lower. Under these circumstances, the Hall current can couple low-frequency Alfvén and magnetoacoustic waves via the dimensionless Hall parameter $\epsilon =\omega /{{\rm{\Omega }}}_{{\rm{i}}}f,$ where ω is the wave frequency and ${{\rm{\Omega }}}_{{\rm{i}}}$ is the mean ion gyrofrequency. This is analyzed in the context of a cold (zero-β) plasma and in less detail for a warm plasma. It is found that Hall coupling preferentially occurs where the wavevector is nearly field-aligned. In these circumstances, Hall coupling in theory produces a continual oscillation between fast and Alfvén modes as the wave passes through the weakly ionized region. At low frequencies (mHz), characteristic of solar and stellar normal modes, epsilon is probably too small for more than a fraction of one oscillation to occur. On the other hand, the effect may be significant at the far higher frequencies (Hz) associated with magnetic reconnection events. In another context, characteristic parameters for star-forming gas clouds suggest that ${\mathcal{O}}(1)$ or more full oscillations may occur in one cloud crossing. This mechanism is not expected to be effective in sunspots, due to their high ion gyrofrequencies and Alfvén speeds, since the net effect depends inversely on both and therefore inverse quadratically on field strength.

AB - The photospheric temperature minimum in the Sun and solar-like stars is very weakly ionized, with an ionization fraction f as low as 10−4. In galactic star-forming regions, f can be 10−10 or lower. Under these circumstances, the Hall current can couple low-frequency Alfvén and magnetoacoustic waves via the dimensionless Hall parameter $\epsilon =\omega /{{\rm{\Omega }}}_{{\rm{i}}}f,$ where ω is the wave frequency and ${{\rm{\Omega }}}_{{\rm{i}}}$ is the mean ion gyrofrequency. This is analyzed in the context of a cold (zero-β) plasma and in less detail for a warm plasma. It is found that Hall coupling preferentially occurs where the wavevector is nearly field-aligned. In these circumstances, Hall coupling in theory produces a continual oscillation between fast and Alfvén modes as the wave passes through the weakly ionized region. At low frequencies (mHz), characteristic of solar and stellar normal modes, epsilon is probably too small for more than a fraction of one oscillation to occur. On the other hand, the effect may be significant at the far higher frequencies (Hz) associated with magnetic reconnection events. In another context, characteristic parameters for star-forming gas clouds suggest that ${\mathcal{O}}(1)$ or more full oscillations may occur in one cloud crossing. This mechanism is not expected to be effective in sunspots, due to their high ion gyrofrequencies and Alfvén speeds, since the net effect depends inversely on both and therefore inverse quadratically on field strength.

KW - ISM: clouds

KW - stars: atmospheres

KW - Sun: helioseismology

KW - Sun: oscillations

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