The Semi-analytic Parker Propagator Solution
Stawicki et al. (2000) found an analytic description for the general solution to the spherical symmetric heliospheric modulation problem.
T:http://articles.adsabs.harvard.edu/pdf/1995ICRC....4..676B
T:https://pdfs.semanticscholar.org/4e95/d1f7cb5d6ee7b763cd99e0a2dfd286b64bba.pdf
https://fenix.tecnico.ulisboa.pt/downloadFile/395144667265/dissertacao.pdf
A good introduction to solar modulation.
T:SOLAR MODULATION MODELS: A COMPARISON THROUGH A 2D STOCHASTIC SIMULATION
the gradient drift could decrease the flux, otherwise the curvature and neutral could increase the flux.
when the cosmic rays enter solar system, they interact with the magnetic field and solar wind from the Sun. The charged particles created by the Sun are called solar wind. The wind blows out with the speed about $400\,\mathrm{km/s}. The magnetic field of the Sun is frozen into the solar wind. The outward solar wind produces a spiral magnetic field structure. This is regular magnetic field.
T:The simulated features of heliospheric cosmic-ray modulation with a time-dependent drift model. IV - The role of heliospheric neutral sheet deformation
Any modulation effects beyond R_b(100AU) were neglected and no termination shock was incorporated because the cosmic-ray energy considered was chosen high enough to neglect the effects of such a shock. Kota(1990) showed that the effects of a termination shock, and the additional modulation one would expected beyond the shock, is negligible for 770 MeV protons but is dramatic for 75 MeV protons.
no qualitative differences and insignificant quantitative differences between the solutions of the 2D and 3D models.
T:
At 1 AU for an observer at the pole and at the equator. The energy loss is substantially less at the pile than at the equator. For the case $qA<0$, we find a similar value for the energy loss at the equator, but the polar energy loss is approximately the same as the equatorial value in this case.
T:A drift model for the modulation of galactic cosmic rays
In the no drift case, near_Earth particles obviously from a wide range of helio-latitude across the boundary, This is due to the diffusive flux perpendicular to the field from pole to ecliptic. For the $qA>0$ drift case this equatorially directed flow is enhanced, to such an extent that most observed particles cross the boundary within ~20 degree off the pole. In the $qA<0$ case, the poleward-directed drift flow evidently exceeds the equatorially directed diffusive flow, so that near Earth particles could only have penetrated the boundary in a narrow range around the ecliptic,
For $A<0$ case, particles crossing the boundary in the polar regions can only reach Earth if the equatorially directed component of the perpendicular diffusive flux can overcome the poleward-directed component of the drift transport. When $k_{\parallel}$ is increased, the density gradients throughout the modulation cavity can relieved. This diminishes both the perpendicular diffusive flux and the drift transport.
The increase in $k_{\parallel}$ also causes an increase in the net radial inward diffusive flux in this narrow range of helio-latitude, which cause the $A<0$ intensity at Earth to increase. In the $A>0$ case, the drift transport from the pole to equator is so effective that virtually all observed particles come from the polar regions. Now, an increase in $k_{\parallel}$ will decrease the effectiveness of this drift transport, and the observed particles of this drift transport, and the observed particles get a much wider region of origin,
The decrease in efficiency of drift transport from pole to equator is offset by so many more particles reaching Earth through diffusive transport from the wider region of origin that the intensities at Earth are minimally affected.
when the magnetic field points outward in the north pole and point inward in the south, we call the polarity is positive ($A>0$). if the magnetic field points inward in the north, the polarity is negative. when the inward and outward magnetic field cancel out, that region is named neutral current sheet.
The change of solar activity have nearly 11-year cycle. The sunspot counts, magnetic field and tilt angle between magnetic axis and rotation axis also have 11-year cycle. They vary from minimum to next minimum about every 11 years.
The solar maximum and solar minimum refer the periods of maximum and minimum sunspot counts. The direction of magnetic field reverse about solar maximum. The recent solar maximum is in April 2014. Now we are in the positive polarity cycle.
The particles experience diffusion, convection, drift and energy loss processes.
The random magnetic field change the particles motion direction. The random walk is described by diffusion (why, random walk equate diffusion).
what's convection? what force makes the particles convection.
The outward solar wind stream results in the particles convection. The particles with speed $v_{sw}$ fly outward the solar system.
The non-homogeneous magnetic field produce the motion of guide center of particles .
Adiabatic compression or compression contributes the energy variation of particles.
what's adiabatic energy loss?
what's diffusion and random walk? Does the random walk means the probability of walk left or right is same ? (NOT!!!)
Diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules or atoms. Diffusion is driven by a gradient in chemical potential of the diffusing species. A distinguishing feature of diffusion is that it depends on particle random walk, and results in mixing or mass transport without requiring directed bulk motion.
In the phenomenological approach, diffusion is the movement of a substance from a region of high concentration to a region of low concentration without bulk motion. According to Fick's laws, the diffusion flux is proportional to the negative gradient of concentrations. It goes from regions of higher concentration to regions of lower concentration.
From the atomistic point of view, diffusion is considered as a result of the random walk of the diffusing particles.
A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a simple random walk, the location can only jump to neighboring sites of the lattice, forming a lattice path. In simple symmetric random walk on a locally finite lattice, the probabilities of the location jumping to each one of its immediate neighbours are the same.
convection, in the wiki
convection is the transport of a substance by bulk motion. The properties of that substance are carried with it. Generally the majority of the advected substance is a fluid.An example of convection is the transport of pollutants or silt in a river by bulk water flow downstream.
Cosmic rays are energetic particles mainly from outside the Solar System.
Propagation inside the solar environment makes the CR spectrum decrease in intensity and change with time. It is called solar modulation.
The difference between the energy spectrum in the heliosphere and the one out of heliosphere is called solar modulation.
The energy spectrum in the heliosphere are affected by the solar activity.
The convection results from the particles move with small scale magnetic field together ?The sunspot is believed a good proxy of solar activity level. The sunspot began decrease from 2002 and reached minimum in 2009. After 2009 the sunspot number increased to maximum in 2014. It decreased again after 2014.
The diffusion results from random walk in the irregular magnetic ? If there is no solar MF, will the random MF be created or not?
If there is no solar MF, do the particles loss energy or not? Are these process created by solar MF ?
We expect the cosmic rays flux have opposite tendency.
PAMELA and AMS-02 measured cosmic rays over a long time. They published some observations.
We can learn the evolution of proton energy spectrum. The flux approached maximum in 2009. Then, as solar activity increases the flux began to decrease.
The cosmic rays propagate in the heliosphere. The heliosphere is a region created by solar wind. The stream of charged particles from solar corona is called solar wind. At the termination shock the solar wind speed slows down to subsonic. Beyond the termination shock, the solar wind speed keeps decrease and stop at a boundary called heliopause.
The cosmic rays in the heliosphere experience four processes.
process in a turbulent magnetic field
convection (because of the motions of the plasma – the solar wind – that fills the heliosphere) and adiabatic energy losses associated to the expansion of the plasma.
The motion of a particle in a non-homogeneous magnetic field can be decomposed into the gyration around the field lines accompanied by the drift of the gyration center in a direction orthogonal to the lines
The diffsuion results from random walk in the irregular MF.
The convection ans energy loss result from the outward solar wind.
