Plasma turbulence and the propagation of charged
particles in the Heliosphere
G.
Erdős, Z. Németh, T. Horbury, S. Dalla, B. Heber, J. Kóta, M. Forman, S.
Oughton
The propagation of energetic particles through complex magnetic fields is an important question in many astrophysical scenarios. Knowledge of the three-dimensional structure of the inteplanetary magnetic field is vital for understanding physical processes in the heliosphere, such as turbulence and energetic particle transport. These two subjects are intimately connected. We propose to use novel and state-of-the-art methods to study the turbulence of the interplaneatry magnetic field and its implication on the propagation of energetic charged particles. Magnetic field and particle observations will be used. The proposed team combines expertize from both areas.
The solar wind is a tenuous (and therefore, collisionless), magnetized plasma, which is highly fluctuating and turbulent. There are evidences that the fluctuations in the solar wind are not just remnants of the waves in the solar corona. Observations have shown that there is an active turbulent cascade in the solar wind, where the wave energy is continuously transferred from the long wavelength mode to the shorter ones. The turbulence seems to be a common phenomenon in many interesting astrophysical objects however, those are unavailable for in situ studies (including the lower solar corona). As a contrast, the solar wind is a very good laboratory to observe MHD turbulence. Therefore, the study of the fluctuations in the solar wind is interesting not only by itself but, it may contribute to the better understanding of a wide range of astrophysical objects.
Knowledge of the three dimensional structure of the magnetic field in the heliosphere is vital for understanding physical processes in the solar system, such as energetic particle propagation and turbulence. These two subjects are intimately linked, since magnetic field fluctuations determine energetic particle trajectories. Particles of different energies are sensitive to the field on different scales, and measurements of particle fluxes can therefore provide information on magnetic structure on many scales, far from the measurement point, while small scale, local magnetic structure can be measured by spacecraft magnetometers. As a result, particle and field data complement each other: a greater understanding of field structure can help in modelling particle transport, while particle measurements can improve field models.
Many questions regarding heliospheric magnetic structure, and particle propagation within it, remain unanswered. However, recent advances in data analysis techniques (fractals; wavelets), theory (spinors; anisotropic turbulence models) and available data (Ulysses at the large scale; Cluster at the small scale) can help to shed light on these problems. The work detailed in this proposal would bring together team members with a wide range of expertise in both data analysis and modelling, of both particle propagation and turbulence, in a timely effort to improve understanding of both magnetofluid turbulence and particle propagation.
The study of the propagation of energetic charged particles through the heliosphere has a long history. Due to substantial fluctuations in the magnetic field, the motion of particles involves diffusion, both parallel and perpendicular to the mean magnetic field direction. Theoretical models which describe the transport of particles regard the diffusion coefficients as phenomenological parameters, which are functions of location in the heliosphere, rigidity of particles, and time. Therefore, to understand the particle propagation more deeply, it would be necessary to derive the diffusion coefficients from the characteristics of the magnetic field fluctuations.
The most widely used model to calculate the parallel diffusion coefficients from magnetic field data is the quasi-linear theory. However, calculations show that this produces estimates of the particle mean free path around an order of magnitude smaller than those measured using observations of solar particle events. Recently, Bieber et al. argued that anisotropy of the turbulence was responsible for this discrepancy. In particular, turbulent fluctuations with wave vectors perpendicular to the magnetic field, which would still be measured by a magnetometer, do not resonate with energetic particles and therefore do not scatter them. This approach holds much promise. However, much more sophisticated analysis of magnetic field data is required. Note, that for perpendicular wave vectors, the ion cyclotron damping, which is thought to be responsible for the dissipation of turbulence at high frequencies, is ineffective therefore, the dissipation mechanism needs further clarification as well.
The scattering of particles perpendicular to the mean magnetic field is even a more difficult problem than the parallel one. That is an important issue, consider only that the galactic cosmic rays enter the inner Heliosphere mostly by crossing magnetic field lines (in the equator because of the Parker winding of the field lines, in the pole because of the large-scale fluctuations of the field). There are several physical mechanisms which might contribute to the off-field motion of particles. One is the separation of adjacent field lines (exponentially with the distance along the lines), this process is an analog of the separation of phase space trajectories at chaos. Also, plasma turbulence results in a mixing of field lines. We address these problems by detailed analysis of observed magnetic field inhomogenities, and by numerical modeling of turbulence.
We would like to use modern data analysis and modeling tools. These include the wavelet and structure function analysis of magnetic field time series, and searching for fractal properties. In addition to the standard quasi-linear method, which corresponds to a perturbation calculation using regular particle trajectories along the main magnetic field, we also use another method which uses curvilinear coordinates attached to the actual (instead of main) magnetic field. This alternative mathematical method (spinor-treatment) offers new insights and new angles to treat random motion in stochastic magnetic fields. Working together of the team members, experienced in various branches of these tools looks stimulating and might give an impetus in the deeper understanding of the problems above.
The proposed research program is timely because of the recently available, qualitatively novel space observations. The team has access in CoI level for that data, which are:
Ulysses magnetic field (MAG) and
energetic particle (KET, AT) measurements:
The Ulysses data is very unique and useful in our study, because the spacecraft has visited unexplored spaces of the Heliosphere (high latitude), during different level of the solar activity (comparison of the first and second orbit). Moreover, the long time that Ulysses has spent in the fast solar wind offers the possibility to study those magnetic field fluctuations which are not contaminated by transient events.
Cluster-II magnetometer:
Cluster offers the first possibility to determine the total tensor of derivatives of the magnetic field. This is an important step forward, since these data are vital for the spinor formalism mentioned above. Cluster will also improve our knowledge on the three dimensional properties of the correlation function of the magnetic field, which is an essential quantity of more advanced particle transport theories.
As seen from the appended Curricula and list of publications, members of the team cover a wide range of expertise in the theory and observation of turbulence in the solar wind as well as transport of energetic particles. Earlier works of the team members include
ˇ the study of the evolution of turbulence in the solar wind
ˇ the observation and modelling of energetic particle fluxes in the heliosphere
ˇ the application of novel data analysis and modeling tools (structure functions, spinor formalism, fractal analysis, wavelet analysis)
ˇ the study of the separation and mixing of magnetic field lines
ˇ the study of the relation between magnetic turbulences and the correspnding particle transport parameters (diffusion coefficients parallel and perpendicular to the mean field).
We hope to achieve advance in some fundamental questions of space plasma physics, including
Papers
to be published: 2-4 in refereed journals
To make significant progress in the joining up of theoretical and experimental work on turbulence and energetic particle propagation, and therefore an increase in our understanding of these phenomena, extended meetings of several days are required in a quiet location: only in this way can information be shared efficiently between members. Such an environment is not available in the institutions of individual members. In addition, the unique funding model of ISSI makes it possible for the members to meet for an extended period: this would simply not be possible anywhere else.
Each team member is highly qualified and internationally recognised in their own speciality. Between them, the team has expertise in measurements of energetic particles and the magnetic field in the heliosphere; advanced data analysis techniques; magnetohydrodynamic turbulence theory; and energetic particle propagation theory, providing a complete range of knowledge necessary to complete this project. The members, and their respective areas of expertise, are:
Dr. Géza Erdős (solar wind observations and analysis)
Dr. Zoltán Németh (fractal analysis)
Dr. Tim Horbury (solar wind observations and analysis)
Dr. Silvia Dalla (energetic particle observations)
Dr. Bernd Heber (cosmic ray observations)
Dr. József Kóta (energetic particle theory and simulation)
Dr. Miriam Forman (energetic particle theory)
Dr. Sean Oughton (MHD turbulence theory)
Two meetings, each of one week in duration, are envisaged. Before the first meeting, team members would identify key problems and opportunities, and how best to make progress.
The first meeting would allow different team members to share knowledge, and also work together: splinter sessions would be likely. We anticipate significant progress, not just information sharing, during this time. A report, compiled at the end of the meeting and presented to ISSI, would summarise progress and plans to proceed before the next meeting. Work towards these goals would be performed by individual team members at their own institution during this time. One of more papers are likely to be written between the two meetings.
The second meeting, around one year after the first, would allow the participants to consolidate work done during the year, perform more work, and prepare joint publications. We also anticipate work progressing after the end of the ISSI workshops, as a result of the greater collaboration between the team members.
During each stay, two meeting rooms (up to ten people) would be required. Computing requirements (internet connectivity, a small number of PCs) are modest, and easily provided by current ISSI facilities, since it is not anticipated that large computations would be performed at ISSI: most members would bring laptops. The team anticipates sharing information via a web page: hosting this at ISSI would be useful.
Travel costs will be met by the institutions of the team members. Accommodation and subsistence costs for the team (8 members) are required, for two meetings. Allowing for Saturday night stay requirements for some travel, a maximum of six nights per person per trip is required, giving a total of 6 nights x 8 people x 2 meetings = 96 man-days total stay, equivalent to about 14 man-weeks. However, we would like to setup a larger margin, and increase this sum up to about 20 man-weeks. The reason is, that we might invite some guests for the second workshop. Also, some of the team members are likely to extend their stay in Bern for longer time to work together. No other costs are anticipated.
Budapest, 2 May 2003
Géza Erdős
lead investigator