This workshop intends to join and exploit state-of-the-art expertise in magnetohydrodynamic (MHD) plasma modeling, and thereby identify the most challenging open questions common to laboratory and astrophysical applications. In a timely follow-up to the ‘Principles of Magnetohydrodynamics’ Lorentz Centre workshop in march 2005, this workshop will center on the invariably multi-disciplinary aspect of current MHD research, where advanced numerical and analytical techniques combine to pursue modern plasma physics research.

The targeted subthemes include:

• Advanced MHD spectroscopy: starting from the most recent insights in linear waves and stability properties of flowing MHD equilibria, where contemporary methods for (quadratic) generalized eigenvalue problems feature in astrophysically relevant configurations, such as solar coronal loops, to magnetized accretion disks and astrophysical jet flows. For the latter application, extensions of proven techniques from non-relativistic to relativistic flow regimes must be initiated. In fusion plasmas, the effect of background flows on the stability of magnetically caged, hot plasmas has only recently witnessed increased attention. Our guiding question will be: Can we compute all eigenoscillations for flowing laboratory as well as astrophysical plasma configurations, and does such knowledge of the entire spectrum of ‘normal’ modes give clues to which mode-mode interactions may prevail in further nonlinear evolutions?

• Computational MHD challenges: identifying the most desired improvements in the main algorithmic strategies for large-scale computing in magneto-fluid dynamics; with coexisting regions of dominant kinetic, thermal and magnetic field energies in scaleencompassing simulations. Here, we also envision to take stock of novel hierarchical algorithms where a multiplicity of discretization schemes, or even multiple physics models are handled, coupling dynamics happening across intrinsically different sizes and timescales. We will discuss: Which plasma dynamical phenomena truly require hybrid, multiple physics approaches, and how does this relate to contemporary coding efforts?

• Contemporary solar and astrophysical research frontiers: where extensions to pure ideal MHD treatments have become essential to confront computational predictions with observational reality. This includes radiative treatments in MHD simulations, as well as relativistic MHD regimes, with applications ranging from solar physics (flux emergence, prominence formation, . . . ) over (proto-)stellar systems (where magnetic fields control star-accretion-disk-jet dynamics), up to the higher and highest energy phenomena in our observable universe (pulsar magnetospheres, magnetars, gamma-ray-burst modeling).Our guiding principle here is: Where do we stand when confronting our simulations with actual data, from solar to extragalactic applications?

The keynote speakers are experts in the field, with proven skills in addressing mixed multidisciplinary  audiences. By realizing a balanced division over PhD, postdoc and advanced researcher participants, we wish to optimize the chances to foster new collaborations between existing research groups. The workshop can be considered succesfull when we, during the discussion sessions, identify conclusive answers to the above three questions, and come up with concrete joint projects that help to get quantitative answers. This also will translate into selected algorithmic challenges that new or existing code efforts need to face in the future. Summaries of the discussions and challenges will be made available at the end of the workshop, and distributed to all participants.