Scaling and a Fokker‐Planck model for fluctuations in geomagnetic indices and comparison with solar wind ε as seen by Wind and ACE

Abstract

[1] The evolution of magnetospheric indices on temporal scales shorter than that of substorms is characterized by bursty, intermittent events that may arise from turbulence intrinsic to the magnetosphere or that may reflect solar wind-magnetosphere coupling. This leads to a generic problem of distinguishing between the features of the system and those of the driver. We quantify scaling properties of short-term (up to few hours) fluctuations in the geomagnetic indices AL and AU during solar minimum and maximum, along with the parameter that is a measure of the solar wind driver. We find that self-similar statistics provide a good approximation for the observed scaling properties of fluctuations in the geomagnetic indices, regardless of the solar activity level, and in the parameter at solar maximum. This self-similarity persists for fluctuations on timescales at least up to about 1-2 hours. The scaling exponent of AU index fluctuations show dependence on the solar cycle, and the trend follows that found in the scaling of fluctuations in . The values of their corresponding scaling exponents, however, are always distinct. Fluctuations in the AL index are insensitive to the solar cycle, as well as being distinct from those in the parameter. This approximate self-similar scaling leads to a Fokker-Planck model which, we show, captures the probability density function of fluctuations and provides a stochastic dynamical equation (

Dynamical critical scaling of electric field fluctuations in the greater cusp and magnetotail implied by HF radar observations of F-region Doppler velocity

“…2). Hnat et al (2003b) also showed the solar wind parameter vB 2 scaled for τ up to 26 h. Given we expect solar cycle variability (Pagel and Balogh, 2002;Hnat et al, 2005) and a particular turbulent regime may not end suddenly, our outer temporal scale, τ ≈9.1 h, is in basic agreement. However, Hnat et al (2002b) obtained α 0 =0.42±0.03 using bin sizes δε which decrease logarithmically with δε, and this disagrees with our initial estimate of α 0 =0.33±0.03.…”

“…Figure 4 illustrates how difficult it is to scale the ε parameter, and suggests caution in making direct comparisons between the absolute values of α 0 obtained for completely different data sets. However, the presence of fluctuations common to the solar wind and electrojet indices can be inferred from relative variations in the corresponding scaling parameters, such as those which depend upon solar phase (Hnat et al, 2005).…”

“…A recent study by Hnat et al (2005) suggests that fluctuations in auroral electrojet indices are partly driven by the solar wind, yet partly independent, hence suggesting selforganised behaviour in the magnetotail. Although some substorms are triggered by IMF northward turnings, and the solar wind may be the ultimate source of energy, it is well known that substorm evolution is not necessarily directly driven by solar wind variability.…”

“…Next we characterise concurrent fluctuations in v LOS by calculating PDFs sorted according to IMF orientation, magnetic local time (MLT), and approximate regions of open and closed magnetic flux. The different sets of PDFs are re-scaled using the generic and model independent techniques described by Hnat et al (2002bHnat et al ( , 2003aHnat et al ( , 2005. The extent to which the PDFs collapse to a common curve reveals whether they are self-affine (mono-fractal, single exponent scaling) or possibly multi-fractal (e.g.…”

Comparison of chaotic aspects of magnetosphere under various physical conditions using AE index time series

“…It is still unclear to what extent the fluctuations in the solar wind are reflected in the fluctuations of magnetosphere-ionosphere system. Numerous studies have tried to approach this problem by using both deterministic and stochastic paradigms (Tsurutani et al, 1990;Hnat et al, 2005;Cheng et al, 2005;Pulkkinen et al, 2006).…”