ISSN 1062-8738, Bulletin of the Russian Academy of Sciences. Physics, 2015, Vol. 79, No. 5, pp. 637–639. © Allerton Press, Inc., 2015. Original Russian Text © A.V. Belov, A.A. Abunin, M.A. Abunina, E.A. Eroshenko, V.A. Oleneva, V.G. Yanke, 2015, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2015, Vol. 79, No. 5, pp. 691–693. 637 INTRODUCTION A magnetic cloud (MC) maintains its solar struc- ture as it approaches the Earth [1]. It was shown in, e.g., [2] that all ICMEs approaching the Earth have a rope structure (a flux rope) that is not visible in some events [2, 3]. The belief that most MCs observed near the Earth have a quasi-cylindrical geometry [2, 4] agrees with concepts of the inner part of a CME being a primary solar filament in the form of a long cylinder (a rope [2, 4]), with observations of solar wind near the Earth, and with successful attempts to model MCs as cylin- drical formations [5]. A small near-Earth portion of a cloud can be visualized as a cylinder, and this model can be used for (among other things) predicting the further development of the disturbance. If the MC is a source of cosmic ray (CR) modulation, a CR density minimum should be observed near the central axis of the cylinder, and the density should increase toward its surface. A parabola is the simplest function capable of describing this distribution. In this work, we apply this model to many MC events and study the effect mag- netospheric variations on CRs. DATA AND METHODS ICMEs included in the MO WIND list (http://wind.nasa.gov/mfi/magcloud_pub1.html) and/or listed in [7] and/or [8] were selected from the ICME catalog [6] for 1996–2009 (the most complete catalog of interplanetary disturbances for these years). The database on Forbush effects (FEs) developed at IZMI- RAN is based on variations in the density and anisot- ropy of CRs with a rigidity of 10 GV, found using the version of the global survey method (GSM) in e.g., [9]. In this work, we consider the behavior of only the iso- tropic part of CR variations, i.e., hourly data on varia- tions in CR density. RESULTS AND DISCUSSION Our ICME sample with MCs observed near the Earth in solar cycles 23–24 included 99 events. The ICME plasma propagates in an almost radial fashion, so the hourly mean data provide an almost radial sec- tion of the density distribution (or, more precisely, a puncture). When modeling hourly mean data, how- ever, we should remember that the Earth travels differ- ent distances per hour in crossing an interplanetary disturbance, depending on the velocity of the relevant part of the event, and the distances for charged parti- cles are measured in gyroradii ρ, rather than in kilo- meters or astronomical units. The gyroradii are deter- mined by particle rigidity R and IMF strength B. An observer covers gyroradii per hour in an interplanetary disturbance, where V is the radial veloc- ity of solar wind. Moving from linear dimensions to gyroradii, the CR density distribution inside an MC is more symmetrical. Magnetospheric variations in CR [10] during mag- netic storms is the second important point to be con- sidered. Most variations are caused by changes in the rigidity of the geomagnetic cutoff at the points of observation, and a variable increment of the count rate that depends on the level of geomagnetic activity appears. The expected variation in CR density inside an MC can thus be written as (1) where a is a constant, b 1 is the trend coefficient, b 2 reflects the main part of the MC effect on CRs, and b d determines the contribution from the magneto- sphere. This simple model was applied to all 99 events, with parameters a, b 1 , b 2 , and b d being determined each time. Figure 1 presents a model representation of vari- ations in CR density inside an MC. X cVB R ρ = δ= + + + Dst 2 1 2 , d a bX bX b Modeling Variations in CR Density in Magnetic Clouds A. V. Belov, A. A. Abunin, M. A. Abunina, E. A. Eroshenko, V. A. Oleneva, and V. G. Yanke Pushkov Institute of Terrestrial Magnetism, the Ionosphere, and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, Troitsk, Moscow oblast, 142190 Russia e-mail: erosh@izmiran.ru Abstract—It is shown that the behavior of the cosmic ray density in a magnetic cloud near the Earth can for most events be described by a simple parabolic dependence on a distance to the cloud’s center, measured in gyro radii. Most magnetic clouds modulate cosmic rays, lowering their density. However, there are events (approximately 1/5) in which the cosmic ray density rises in a magnetic cloud. Events with the positive effect usually have a maximum in the leading part of the cloud. Several factors are considered that contribute to a model description, and these contributions are estimated. DOI: 10.3103/S1062873815050159