New insights from modeling the neutral heliospheric current sheet

Abstract

Recently, the modulation of cosmic rays in the heliosphere has increasingly been studied by solving the well known transport equation via an approach based on stochastic differential equations. This approach, which is now wellestablished and published, allows for an in depth study of the modulation effects of the wavy heliospheric current sheet, in particular as its waviness increases with solar activity up to extreme maximum conditions. This is possible because of the numerical stability of the approach as well as its ability to trace pseudo-particles so that insightful trajectories of how they respond to the wavy heliospheric current sheet can be computed and displayed. Utilising such a stochastic model, we present valuable new insights into how the geometry of the wavy current sheet can affect the modulation of cosmic rays, especially at the highest levels of solar activity. This enables us to show, from a modeling perspective, why a certain choice for the current sheet profile is more suited than another at these high solar activity levels. We emphasise the importance of an effective tilt angle and illustrate how this concept can be employed effectively in interpreting results pertaining to the wavy current sheet as well as the modulation associated with this important heliospheric structure.

Cosmic-Ray Transport in Heliospheric Magnetic Structures. II. Modeling Particle Transport through Corotating Interaction Regions

“…The numerical code is based on Kopp et al (2012), wheredetails about the method and its numerical realization can alsobe found. Equation (1) has to be transferred to a system of Langevin-type equations, which can be found, e.g., in Strauss et al (2012) or Raath et al (2015Raath et al ( , 2016 and consist each of a deterministic convective part and a stochastic diffusive part.…”

“…For a discussion of alternative formulations,see Raath et al (2015). The constant j 0 and the tilt angle α were determined by fitting the analytical configuration to the CRONOS output.…”

Charge-sign dependent modulation of cosmic ray electrons and positrons up to extreme solar maximum conditions

“…This closing up of the loop between the solutions for the A > 0 and A < 0 polarity cycles that occurs at the theoretical maximum of α = 90 • is a property of our model [12,13]. In this work, we close the loop at a lower value of α = 75 • , since calculations based on observations never show values higher than this (see Figure 4).…”

“…it is inversely proportional to the magnitude of the HMF. The features and properties of the model are discussed in detail by [12,13].…”

“…We use a different type of numerical model: one based on the solution of an appropriate set of stochastic differential equations (SDEs). This model has its roots in that of [15,16] and has been applied to various aspects of solar modulation recently by [12,13]; see also the detailed discussion of the mathematics and practical implementations of SDEs by [5].…”