Simple analytical solutions for propagating diffusive barriers and application to the 1974 minicycle

Abstract

Abstract. The cosmic ray minicycle of 1974 is a medium-term modulation event where a clear anticorrelation is observed between the cosmic ray intensity and the heliospheric magnetic field magnitude B. It occurs during a period of minimum solar activity in an A > 0 magnetic polarity epoch. Cosmic ray modulation during the event is studied with an analytical, spherically symmetric approximation for a propagating diffusive barrier. Under the assumption that the cosmic ray radial diffusion coefficient K scales inversely with B, the temporal development of the disturbance can be obtained from the observed variation of B. A recovery process is described by a simple exponential, with a constant recovery time throughout the event. The profile of the intensity decrease as predicted by the model varies with the temporal development of the disturbance and with the duration of the disturbance in relation to the recovery timescale. The model predicts a maximum depression which is about a factor of 2.5 too small compared with neutron monitor observations. A replacement of the inverse relation K cr lIB by the more general case K cr B -• and a value of n • 2.5 leads to a good agreement between model and observations. It is remarkable how closely the high-energy cosmic ray intensity follows the temporal structure of the magnetic field magnitude, suggesting that the magnetic field enhancement plays an important role for modulation during the minicycle. For the period under study, radial diffusion is essentially determined by diffusion parallel to the average field. Based on quasilinear theory a variation Kii cr B -2 is suggested, consistent with the value of n -2.5 q-1.0 derived in the paper.

Oscillations in the open solar magnetic flux with a period of 1.68 years: imprint on galactic cosmic rays and implications for heliospheric shielding

“…As a consequence of this, recent works in the literature have used these anti-correlations to investigate the effect of solar modulation of GCRs using simpler concepts than the full Parker equation. For example, Wibberenz et al (2002) assumed that the radial diffusion coefficient scales as some power of the magnitude of the IMF and invoked continuous recovery processes (related to particle entry into depleted regions of the heliosphere by drift and diffusion), to develop a simple model which seems to map cosmic ray intensity variations very well over the last four solar cycles (Wibberenz and Cane, 2000;Wibberenz et al, 2002). In their model, the initial cosmic ray intensity, assumed to be a steady-state solution of a spherically symmetric approximation, is perturbed by increases in the IMF that propagate away from the Sun and cause a reduction in the GCR radial diffusion coefficient.…”

Charge-sign dependent modulation in the heliosphere over a 22-year cycle

“…These simulations were generally done for radial distances larger than 20 AU, allowing enough time for merging of corotating structures to take place. More recently, Cane et al (1999) and Wibberenz and Cane (2000) argued that the cosmic ray step decreases observed at Earth cannot be caused by GMIRs because these decreases occurred before any GMIRs could form beyond 10-20 AU. Instead, they suggested that time-dependent global changes in the heliospheric magnetic field (HMF) might be responsible for long-term modulation.…”

Modulation of Cosmic‐Ray Electrons in a Nonspherical and Irregular Heliosphere

“…For the transport model a tilt angle ¼ 20 (Hoeksema 1992) was assumed, indicating a well-organized heliosphere. Figure 2b is shown for reference and illustrative purposes only and is similar to Figure 2a Figure 2c is similar to Figure 2b, except ¼ 60 in the transport model, to simulate moderate solar maximum conditions without complicating propagating diffusive barriers (e.g., Burlaga et al 1993) and long-term changes in the global HMF strength (Cane et al 1999;Wibberenz & Cane 2000).…”