1. Using 3D Tracer we calculated I for particles starting at local noon, for 2 initial pitch angles (30 o and 60 o ), 4 initial distances (5 – 8 R E ) and for 12 initial particle gyrophases (0 o – 330 o ). For each pitch angle we plotted the values of I for each initial distance and initial gyrophase, using different colours for each of the 4 different initial particle distances (plots 1 and 3). The x-axis corresponds to the azimuth angle of the position of the particle. In the resulting plot we marked with a solid vertical line of the corresponding colour the point were I stopped being relatively constant. We also marked with a dashed line of the same colour the point were I returned to having a constant value. We plotted the regions were I remained constant in plots 2 and 4, using the same colours for each initial distance as in plots 1 and 3. In the case of the 30 o initial pitch angle, I remains constant throughout the path of the particle around the Earth for an initial particle distance of 5 R E. For the other initial distances there appears a region at the night side where I is no longer constant. This region becomes larger further away. In the case of the 60 o initial pitch angle, I remains constant throughout the path of the particle around the Earth for initial particle distances of 4 and 5 R E. Similar to the case of a 30 o initial pitch angle particle there are regions where I is not constant and these regions are larger the longer the initial distance. Generally, the extent of these regions is smaller in the case of the 60 o initial pitch angle particle. We use a particle-tracing model that directly integrates the Lorentz-force equation in a TS05 magnetic field model to compute the second (J) and third (Φ) adiabatic invariants of particle motion as well as Roederer’s L* and the Invariant Integral I, and we compare these computations with approximations made through the neural- network-based method LANL* V2.0 [Koller and Zaharia, 2011], the IRBEM library (International Radiation Belt Environment Modeling library; ex-ONERA-DESP lib) [Bourdarie et al., 2008], and SPENVIS (Space Environment Information System) [Heynderickx et al., 2005]. L* is calculated at different particle initial locations and I also for various pitch-angles. Finally we investigate variations in I throughout a particle’s drift-shell for a set of initial particle phases and pitch angles at various locations, and we comment on the breaking of its invariance. Calculations and comparisons of the adiabatic invariants and L* using a particle-tracing model, LANL*, IRBEM-lib and SPENVIS K. Konstantinidis 1,2, T. E. Sarris 1,2 [1] Democritus University of Thrace, Space Research Laboratory, Xanthi, Greece, kkonst@ee.duth.gr, tsarris@ee.duth.grkkonst@ee.duth.gr [2] Laboratory for Atmospheric and Space Physics, Univ. of Colorado, Boulder, Colorado, sarris@lasp.colorado.edu Laboratory for Atmospheric and Space Physics, CU, Boulder, Colorado REGIONS OF BREAKING OF THE SECOND ADIABATIC INVARIANT ABSTRACT CALCULATIONS OF L* Space Research Laboratory Democritus Univ. of Thrace, Xanthi, Greece Particle Trace, R i = 5 Re Models used: 3D Tracer is a particle tracing code we developed in Fortran. As a model for the magnetic field we used the TS05 external and IGRF internal fields from the Fortran subroutine package provided by Tsyganenko et al. LANL* V2.0 [Koller and Zaharia, 2011] is an artificial neural network (ANN) for calculating the magnetic drift invariant, L*, based on the TS05 model. IRBEM library (ex ONERA-DESP library) [Bourdarie et al., 2008] allows to compute, among other things I and L*. We used TS05 as the external field model and IGRF as the internal field model. SPENVIS [Heynderickx et al., 2005] provides access to models of the hazardous space environment through a user-friendly World Wide Web interface. Among these models is the TS05 and IGRF models. We used SPENVIS to calculate I, L* and Φ. CALCULATIONS OF I We calculated I using each of the above models and for particles starting at local noon, for 2 initial pitch angles (30 o and 60 o ) and 5 initial distances (4 – 8 R E ), as for L* above. Using the 3D Tracer we calculated I for 12 initial particle gyrophases, as above, and calculated the median and σ of I for all gyrophases. There is great coincidence in the calculations of I between all three models for both initial pitch angles. Using each of the above models we calculated L* for particles starting at local noon, for 3 initial pitch angles (30 o, 60 o and 90 o ) and 5 initial distances (4 – 8 R E ). Using the 3D Tracer we calculated Φ and then L* for 12 initial particle gyrophases (0 o – 330 o ). L* for a given distance was then calculated as the median of L* for all gyrophases. The error bars represent 1σ of L* calculations for the 12 gyrophases. Generally, the results from all the models tend to agree more at smaller distances (4 – 6 R E ) and less further away (7 – 8 R E ). Also, the smaller the initial pitch angle is, the greater the spread of the calculated L*. The results from the 3D Tracer tend to agree more with those from SPENVIS, as do the results from IRBEM LIB with those from LANL*. The calculations from LANL* seem to deviate significantly from those from the other models, except from the case of a 90 o initial pitch angle. Adiabatic invariants: Integral invariant coordinate I: For slow drift conditions, the second adiabatic invariant and the integral invariant coordinate I are given, respectively, by: and, where In 3D Tracer we calculate I by integrating along one bounce motion, according to the second formula above. Roederers L*: For slow drift conditions, the drift invariant, Φ, and Roederers L* (L- star) are given, respectively, by: and In 3D Tracer we first integrate the first equation above for one full revolution of the particle around the Earth to calculate Φ, and then we calculate L* using the second equation above. α 0 = 90 ο α 0 = 60 ο α 0 = 30 ο α 0 = 60 ο α 0 = 30 ο α 0 = 30 o α 0 = 60 o 5 R E 6 R E 7 R E 8 R E 5 R E 6 R E 7 R E 8 R E REFERENCES: 1. N.A. Tsyganenko et al., 2008, geo.phys.spbu.ru/~tsyganenko/Geopack-2008.htmlgeo.phys.spbu.ru/~tsyganenko/Geopack-2008.html 2. Koller and Zaharia, 2011, www.lanlstar.lanl.gov/download.shtmlwww.lanlstar.lanl.gov/download.shtml 3. Bourdarie et al., 2008, irbem.svn.sourceforge.net/viewvc/irbem/trunkirbem.svn.sourceforge.net/viewvc/irbem/trunk 4. Heynderickx et al., 2005, www.spenvis.oma.bewww.spenvis.oma.be Plot 1 Plot 2 Plot 3 Plot 4 5 R E 6 R E 7 R E 8 R E