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cosmic rays ( crs ) interacting with turbulent magnetic fields get scattered and accelerated ( see melrose 1968 , schlickeiser 2002 ) .
the theoretical description of these scattering and acceleration processes are essential for understanding the penetration and modulation of low - energy cosmic rays in the heliosphere , the confinement and escape of galactic cosmic rays from the galaxy , and the efficiency of diffusive shock acceleration mechanisms .
a key factor in cr scattering are the properties of the magnetic fields .
a standard approach is the assumption of a superposition of a mean magnetic field @xmath0 and a turbulent component @xmath1 . whereas the mean field
can easily be meassured in the solar system ( here we find approximatelly @xmath2 ) , the turbulent component has to be emulated by turbulence models . in the literature
there is no consensus available about the true turbulence properties ( see cho & lazarian 2005 for a review ) . in the solar system , however , some turbulence properties such as the wave spectrum can be obtained from meassurements ( see e.g. denskat & neubauer 1983 , bruno & carbone 2005 )
.    more unclear are the orientation of the turbulence wave vectors ( also refered to as turbulence geometry ) and the dynamical decorrelation of the magnetic fields . in a recent cr diffusion study ( shalchi et al .
2006 ) a slab/2d composite model was combined with a nonlinear anisotropic dynamical turbulence ( nadt ) model .
this model can be used to reproduce meassured cr mean free paths parallel and perpendicular to the mean field @xmath3 .
the authors of this article assumed that the slab correlation time scale is independent of the wave vector @xmath4 .    in a recent study ( lazarian & beresnyak 2006 )
, however , it was shown that the slab time scale is indeed @xmath5dependent .
more precisely it was found that @xmath6 ; here we used the correlation time @xmath7 , the correlation rate @xmath8 , the alfvn speed @xmath9 , and the outer scale of the turbulence @xmath10 .
it is the purpose of this article to apply this new result of the slab correlation time scale onto cosmic ray parallel diffusion .
a comparison with solar wind observations of the parallel mean free path is also presented .
it is demonstrated that we can find a much larger parallel mean free path if we employ the correlation time scale of lazarian & beresnyak ( 2006 ) .    in section 2
we explain the turbulence model that is used in this article . in section 3 a quasilinear description of cosmic ray scattering
is combined with this turbulence model to derive analytic forms of the pitch - angle diffusion coefficient and the parallel mean free path . in section 4
we evaluate these formulas numerically to compute diffusion coefficients and we also provide a comparison with previous results and solar wind observations . in the closing section 5
our results are summerized .
the key input into a cosmic ray transport theory like qlt is the tensor @xmath11 which describes the correlation of the turbulent magnetic fields : p_lm ( , t ) = therefore the @xmath4-dependence and the time - dependence of the correlation tensor @xmath12 have to be specified which is done in the next two subsections .      for mathematical simplicity
we employ the often used slab model for the turbulence geometry .
physical processes that can induce slab modes are differential damping of fast mode waves ( yan & lazarian 2002 ) or instabilities ( lazarian & beresnyak 2006 ) .    by assuming the same temporal behavior of all tensor components we have p_lm ( , t ) = p_lm^slab ( ) ^slab ( k_,t ) [ c2e2 ] with the dynamical correlation function @xmath13 and the time independent correlation tensor @xmath14 .
the tensor @xmath14 is determined by the turbulence geometry and the wave spectrum whereas the function @xmath15 describes dynamical effects .
for pure slab turbulence we have @xmath16 and therefore p_lm^slab ( ) & = & g^slab(k _ ) ( k _ ) k _ + & & \ {    ccc _ lm - k_l k_m k^2 & if & l , m = x , y + 0 & if & l or m = z    .
[ c2e3 ] in eq .
( [ c2e3 ] ) we assumed the case of vanishing magnetic helicity .
the function @xmath17 is the slab wave spectrum which can be approximated by a power - law spectrum with energy , inertial , and dissipation range ( see fig .
1 ) : & & g^slab ( k _ ) = c ( ) 2 l_slab b_slab^2 + & & \ {    ccc 0 & for & 0 k _
< k_min + ( 1 + k_^2 l_slab^2)^- & for & k_min k _
< k_d + ( 1+k_d^2 l_slab^2)^- ( k_d / k_)^p & for & k_d k _ +    . [ c2e5 ] where we used the normalization function c ( ) = 1 2 ( ) ( - 1/2 ) .
furthermore , we used the slab bendover scale @xmath18 , the dissipation wavenumber @xmath19 , the turbulence strength @xmath20 , the inertial range spectral index @xmath21 and the dissipation range spectral index @xmath22 .
the parameter @xmath23 indicates the smallest wavenumber .
also the dynamical correlation function @xmath13 has to be determined which is done in the next subsection .      in the past several models
have been developed to approximate the dynamical correlation function @xmath13 ( e.g. schlickeiser & achatz 1993 , bieber et al .
1994 , shalchi et al .
some examples are given in table [ tab1 ] .
.previous models for the slab dynamical correlation function . here
@xmath9 is the alfvn velocity , @xmath24 is a parameter which allows to adjust the strength of dynamical effects , and @xmath25 is used in the nadt ( nonlinear anisotropic dynamical turbulence)-model ( @xmath26 ) . [
cols="<,<",options="header " , ]     [ tab2 ]      fig .
[ nadtf23 ] shows the ( dimensionless ) pitch - angle fokker - planck coefficient @xmath28 as a function of the pitch - angle - cosine @xmath29 . for the rigidity we assumed @xmath30 . in this case the parameter @xmath31 ( see eq .
( [ c6e1 ] ) ) is approximately @xmath32 .
it seems that the minimum of the pitch - angle fokker - planck coefficient for protons can be found at @xmath33 .    in general the pitch - angle fokker - planck coefficient
is no longer equal to zero at @xmath34 ( @xmath35 ) as in the magnetostatic model , so that we no longer obtain an infinitely large parallel mean free path as in magnetostatic models .
it should be noted , however , that qlt itself is questionable close to @xmath34 . by considering fig .
[ nadtf23 ] we find that at least for protons pitch - angle scattering close to @xmath34 is very strong due to the dynamical effects
. therefore one could assume that nonlinear effects which also lead to nonvanishing pitch - angle scattering at @xmath34 could be neglected .
here we present theoretical results for the parallel mean free path .
we compare our results with the palmer consensus ( palmer 1982 ) and pickup ion observations ( gloeckler et al .
1995 , mbius et al .
1998 ) . in fig .
[ nadtf4 ] we show the parallel mean free path in comparison with observations .
we computed the parallel mean free paths for two different values of the smallest wave number @xmath37 , namely for @xmath38 and @xmath39 .
in addition to the palmer ( 1982 ) results we compare our results also with pickup ion observations :    1 .
gloeckler et al .
( 1995 ) concluded from ulysses observations that the parallel mean free paths of pickup protons is 2 au at 2.4 mv rigidity ( they stated conservatively that @xmath36 is of order 1 au but actually they obtained the best fit for 2 au ) . it should be noted that this observation was at high heliographic latitudes , and at a heliocentric distance of 2.34 au ; these differences should be remembered when comparing with observations at earth orbit .
2 .   mbius et al .
( 1998 ) concluded from ampte ( active magnetospheric particle tracer explorers ) spacecraft observations that the parallel mean free paths of pickup helium ranges from 0.16 to 0.76 au at 5.6 mv rigidity in the data they analyzed .
both results are also illustrated in fig .
[ nadtf4 ] .
as shown we can reproduce the observations theoretically . in fig .
[ nadtf6 ] we compare our new theoretical results with the results obtained by shalchi et al .
( 2006 ) by applying the nadt - model in combination with the slab/2d model for the turbulence geometry .
as shown , for small rigidities , where dissipation effects are important , we obtain a much larger parallel mean free path for electrons . for medium rigidities where the charged particles interact resonantly with the inertial range of the spectrum , the new parallel mean free path is about a factor 5 smaller since we assumed pure slab fluctuations ( in comparison to the slab/2dspace . ]
model used in shalchi et al .
it seems that the improved model for the slab correlation function provides a much larger electron parallel mean free path for low energetic particles .
the theoretical explanation of measured parallel mean free paths in the solar system is a fundamental problem of space science . in a recent article ( shalchi et al .
2006 ) it has been demonstrated the these observations can indeed be reproduced theoretically . by using recent results of turbulence theory ( lazarian & beresnyak 2006 ) we further improved the dynamical correlation function which is a key input in transport theory considerations .
it is demonstrated in this article that the improved slab correlation time scale ( see eq .
( [ alexmodel ] ) ) leads to a much larger parallel mean free path ( see fig . [ nadtf4 ] ) .
this effect is important since it was argued in several previous articles that the theoretical parallel mean free path is too small ( palmer 1982 , bieber et al .
1994 ) in comparison with solar wind observations .
another problem of cosmic ray scattering theory is the importance of nonlinear effects .
whereas we have applied qlt in the current article it was argued in other papers ( e.g. shalchi et al .
2004 ) that nonlinear effects are important for parallel diffusion . however , these nonlinear effects are directly related to the interaction between charged particles and 2d modes .
these 2d modes were neglected since we assumed pure slab fluctuations .
therefore , qlt can be applied and the results presented in this article should be valid . for non - slab models , where 2d modes are present , however , the applicability of qlt is questionable .
it has to be subject of future work to explore the validity of qlt for realistic turbulence models such as dynamical turbulence models in non - slab geometry .
this research was supported by deutsche forschungsgemeinschaft ( dfg ) under the emmy - noether program ( grant sh 93/3 - 1 ) .
this work was also supported by the nasa grant x5166204101 , the nsf grant atm-0648699 , and the nsf center for magnetic self organization in laboratory and astrophysical plasmas .
this work is the result of a collaboration between the university of bochum , theoretische physik iv and the university of wisconsin - madison , department of astronomy .
by applying recent results for the slab correlation time scale onto cosmic ray scattering theory , we compute cosmic ray parallel mean free paths within the quasilinear limit . by employing these results 
 onto charged particle transport in the solar system , we demonstrate that much larger parallel mean free paths can be obtained in comparison to previous results . a comparison with solar wind observations is also presented to show that the new theoretical results are much closer to the observations than the previous results .    cosmic rays  turbulence  diffusion