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Applying the cold plasma dispersion relation to whistler mode chorus waves: EMFISIS wave measurements from the Van Allen Probes.

Hartley DP, Chen Y, Kletzing CA, Denton MH, Kurth WS - J Geophys Res Space Phys (2015)

Bottom Line: Results from this study indicate that the calculated wave intensity is least accurate during periods of enhanced wave activity.For observed wave intensities >10(-3) nT(2), using the cold plasma dispersion relation results in an underestimate of the wave intensity by a factor of 2 or greater 56% of the time over the full chorus wave band, 60% of the time for lower band chorus, and 59% of the time for upper band chorus.Hence, during active periods, empirical chorus wave models that are reliant on the cold plasma dispersion relation will underestimate chorus wave intensities to a significant degree, thus causing questionable calculation of wave-particle resonance effects on MeV electrons.

View Article: PubMed Central - PubMed

Affiliation: Physics Department, Lancaster University Lancaster, UK.

ABSTRACT

Most theoretical wave models require the power in the wave magnetic field in order to determine the effect of chorus waves on radiation belt electrons. However, researchers typically use the cold plasma dispersion relation to approximate the magnetic wave power when only electric field data are available. In this study, the validity of using the cold plasma dispersion relation in this context is tested using Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) observations of both the electric and magnetic spectral intensities in the chorus wave band (0.1-0.9 f ce). Results from this study indicate that the calculated wave intensity is least accurate during periods of enhanced wave activity. For observed wave intensities >10(-3) nT(2), using the cold plasma dispersion relation results in an underestimate of the wave intensity by a factor of 2 or greater 56% of the time over the full chorus wave band, 60% of the time for lower band chorus, and 59% of the time for upper band chorus. Hence, during active periods, empirical chorus wave models that are reliant on the cold plasma dispersion relation will underestimate chorus wave intensities to a significant degree, thus causing questionable calculation of wave-particle resonance effects on MeV electrons.

No MeSH data available.


Related in: MedlinePlus

The magnetic field power spectral density in the chorus wave frequency band (between 0.1 and 0.9 fce) as measured by EMFISIS on board Van Allen Probe A (blue) and as calculated using the cold plasma dispersion relation (red) at (a) 12:01:41, (b) 11:21:47, and (c) 12:00:11 on 20 November 2012. The normalized root-mean-square errors (NRMSE) are also listed.
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fig02: The magnetic field power spectral density in the chorus wave frequency band (between 0.1 and 0.9 fce) as measured by EMFISIS on board Van Allen Probe A (blue) and as calculated using the cold plasma dispersion relation (red) at (a) 12:01:41, (b) 11:21:47, and (c) 12:00:11 on 20 November 2012. The normalized root-mean-square errors (NRMSE) are also listed.

Mentions: As a test of the methodology described above, the measured power spectral density is compared to that calculated using the cold plasma dispersion relation. Figure 2 displays the power spectral density of the wave magnetic field in the chorus wave frequency range as measured by EMFISIS (blue) and as calculated using the cold plasma dispersion relation (red) for three instances of time. The normalized root-mean-square (RMS) deviations are also listed. For the first time instance, 12:01:41 on 20 November 2012 (Figure 2a), using the cold plasma dispersion relation allows for the magnetic field power spectral density between 0.1 and 0.9 fce to be accurately calculated. That is, the red and blue lines shown in Figure 2a match extremely well. Both upper and lower band chorus waves are apparent during this period with a gap between the two at approximately half of the electron gyrofrequency. The normalized RMS error is very low for this time instance (0.111). For the second instance of time, 11:21:47 on 20 November 2012 (Figure 2b), using the cold plasma dispersion relation results in the calculated power spectral density being around 1 order of magnitude less than that observed across the entire lower band chorus wave frequency range. That is, the red line in Figure 2b is significantly lower than the blue line over the entire 0.1–0.5 fce frequency range. The normalized RMS error for this time instance is 0.287. For the third time instance, 12:00:11 on 20 November 2012 (Figure 2c), the shape of the calculated power spectral density does not quite match that observed by EMFISIS. That is, in contrast to the systematic shift in power spectral density shown in Figure 2b, the discrepancies in this case are frequency dependent. At some frequencies the calculated power spectral density is greater than that observed, and at other frequencies the calculated power spectral density is less than that observed. The normalized RMS error for this time instance is 0.217. Discrepancies between the observed and calculated quantities, such as those shown in Figures 2b and 2c, will certainly affect the calculated integral magnetic field wave intensity, . Cases similar to those shown in Figure 2b (systematic shift) will result in significant errors in the calculated chorus wave intensity. Cases similar to those shown in Figure 2c (frequency-dependent error) may result in errors in the calculated chorus wave intensity; however, it is also possible that when integrated to calculate the wave intensity in the chorus frequency range, the discrepancies could cancel out resulting in the calculated wave intensity matching that measured by the Van Allen Probes. Despite the normalized RMS errors shown in Figures 2b and 2c being approximately equal, in cases similar to that shown in Figure 2c it is likely that the calculated integral wave intensity will be less affected by these deviations in comparison to cases similar to that presented in Figure 2b.


Applying the cold plasma dispersion relation to whistler mode chorus waves: EMFISIS wave measurements from the Van Allen Probes.

Hartley DP, Chen Y, Kletzing CA, Denton MH, Kurth WS - J Geophys Res Space Phys (2015)

The magnetic field power spectral density in the chorus wave frequency band (between 0.1 and 0.9 fce) as measured by EMFISIS on board Van Allen Probe A (blue) and as calculated using the cold plasma dispersion relation (red) at (a) 12:01:41, (b) 11:21:47, and (c) 12:00:11 on 20 November 2012. The normalized root-mean-square errors (NRMSE) are also listed.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4497456&req=5

fig02: The magnetic field power spectral density in the chorus wave frequency band (between 0.1 and 0.9 fce) as measured by EMFISIS on board Van Allen Probe A (blue) and as calculated using the cold plasma dispersion relation (red) at (a) 12:01:41, (b) 11:21:47, and (c) 12:00:11 on 20 November 2012. The normalized root-mean-square errors (NRMSE) are also listed.
Mentions: As a test of the methodology described above, the measured power spectral density is compared to that calculated using the cold plasma dispersion relation. Figure 2 displays the power spectral density of the wave magnetic field in the chorus wave frequency range as measured by EMFISIS (blue) and as calculated using the cold plasma dispersion relation (red) for three instances of time. The normalized root-mean-square (RMS) deviations are also listed. For the first time instance, 12:01:41 on 20 November 2012 (Figure 2a), using the cold plasma dispersion relation allows for the magnetic field power spectral density between 0.1 and 0.9 fce to be accurately calculated. That is, the red and blue lines shown in Figure 2a match extremely well. Both upper and lower band chorus waves are apparent during this period with a gap between the two at approximately half of the electron gyrofrequency. The normalized RMS error is very low for this time instance (0.111). For the second instance of time, 11:21:47 on 20 November 2012 (Figure 2b), using the cold plasma dispersion relation results in the calculated power spectral density being around 1 order of magnitude less than that observed across the entire lower band chorus wave frequency range. That is, the red line in Figure 2b is significantly lower than the blue line over the entire 0.1–0.5 fce frequency range. The normalized RMS error for this time instance is 0.287. For the third time instance, 12:00:11 on 20 November 2012 (Figure 2c), the shape of the calculated power spectral density does not quite match that observed by EMFISIS. That is, in contrast to the systematic shift in power spectral density shown in Figure 2b, the discrepancies in this case are frequency dependent. At some frequencies the calculated power spectral density is greater than that observed, and at other frequencies the calculated power spectral density is less than that observed. The normalized RMS error for this time instance is 0.217. Discrepancies between the observed and calculated quantities, such as those shown in Figures 2b and 2c, will certainly affect the calculated integral magnetic field wave intensity, . Cases similar to those shown in Figure 2b (systematic shift) will result in significant errors in the calculated chorus wave intensity. Cases similar to those shown in Figure 2c (frequency-dependent error) may result in errors in the calculated chorus wave intensity; however, it is also possible that when integrated to calculate the wave intensity in the chorus frequency range, the discrepancies could cancel out resulting in the calculated wave intensity matching that measured by the Van Allen Probes. Despite the normalized RMS errors shown in Figures 2b and 2c being approximately equal, in cases similar to that shown in Figure 2c it is likely that the calculated integral wave intensity will be less affected by these deviations in comparison to cases similar to that presented in Figure 2b.

Bottom Line: Results from this study indicate that the calculated wave intensity is least accurate during periods of enhanced wave activity.For observed wave intensities >10(-3) nT(2), using the cold plasma dispersion relation results in an underestimate of the wave intensity by a factor of 2 or greater 56% of the time over the full chorus wave band, 60% of the time for lower band chorus, and 59% of the time for upper band chorus.Hence, during active periods, empirical chorus wave models that are reliant on the cold plasma dispersion relation will underestimate chorus wave intensities to a significant degree, thus causing questionable calculation of wave-particle resonance effects on MeV electrons.

View Article: PubMed Central - PubMed

Affiliation: Physics Department, Lancaster University Lancaster, UK.

ABSTRACT

Most theoretical wave models require the power in the wave magnetic field in order to determine the effect of chorus waves on radiation belt electrons. However, researchers typically use the cold plasma dispersion relation to approximate the magnetic wave power when only electric field data are available. In this study, the validity of using the cold plasma dispersion relation in this context is tested using Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) observations of both the electric and magnetic spectral intensities in the chorus wave band (0.1-0.9 f ce). Results from this study indicate that the calculated wave intensity is least accurate during periods of enhanced wave activity. For observed wave intensities >10(-3) nT(2), using the cold plasma dispersion relation results in an underestimate of the wave intensity by a factor of 2 or greater 56% of the time over the full chorus wave band, 60% of the time for lower band chorus, and 59% of the time for upper band chorus. Hence, during active periods, empirical chorus wave models that are reliant on the cold plasma dispersion relation will underestimate chorus wave intensities to a significant degree, thus causing questionable calculation of wave-particle resonance effects on MeV electrons.

No MeSH data available.


Related in: MedlinePlus