Current Projects

  Negative effective magnetic pressure

Framework: magnetic flux concentrations on the Sun.
Collaborators: Axel Brandenburg, Nathan Kleeorin, Igor Rogachevskii

Solar and stellar observations have shown us the presence of surface magnetic flux concentrations on intermediate time and length scales. A solid theory that explains their occurence does not exist. In this project we aim to find a mechanism which operates in a turbulent environment and which could redistribute magnetic flux into large scale concentrations.

Magnetic fields act on motions through the Lorentz force, this is true for large and small scale motions, as such one can wonder how the presence of a magnetic field would affect the Reynolds stress tensor. Analytical calculations show the possibility of a reduction of the turbulent pressure to the extent that the total contribution of the magnetic field to the pressure can become negative, hence the name 'negative magnetic pressure'-effect.
This negative feedback of magnetic fields on the pressure can be illustrated as follows: On one hand, it was found that turbulent energy is approximately conserved for field strengths below equipartition, on the other hand we have that the turbulent magnetic field contributes to a lesser extent to the turbulent pressure than its kinetic counterpart, as such for the same turbulent energy the pressure will be lower if there are more magnetic fluctuations.
This effective magnetic pressure was calculated in direct numerical simulations under various conditions and indeed shows this reduction. In a first order model, the effect can be quantified as a correction on the Maxwell stress tensor, the symmetric contribution is quantified by q_p the antisymmetric part by q_s. The latter was shown to be approximately zero in all simulations so far. The former depends on the ratio of the magnetic field to the equipartition field, as well as on the magnetic Reynolds and Prandtl number and is strongly reduced in the presence of small scale dynamo action.

Putting this first order model into a mean-field calculation we expect a negative effective magnetic pressure instability (NEMPi) develop: a locally enhanced magnetic field reduces the pressure, the resulting inflow drags along frozen in magnetic field which in turn reinforces the present field until the point is reached where the feedback reverses. In mean-field simulations these concentrations of magnetic flux indeed grow exponentionally until saturation sets in. The growth rate appears to be a complex function of stratification strength, imposed field, turbulent diffusion,...
Interesting is that for q_s=0 the problem becomes two-dimensional, reducing computational time for mean field runs and allowing us to average along the direction of the imposed field in direct simulations. For a long time the instability was not seen in direct simulations as a result of small scale separation however recent results with larger separation show a clear effect.

In order not to trouble our view and for computational reasons, the included physics in this work were reduced and the setup simplified.
These issues will be dealt with in a later stage of our learning curve, e.g. stratification profile, boundary conditions and radiation.

Normalised effective magnetic pressure as a function of the local ratio of the mean field to the equipartition field strength
(Rm=18, Pm=.5, 256^3 DNS)

Magnetic field (left) and normalised effective magnetic pressure(right) in a plane perpendicular to the applied field at different times
(Rm=18, Pm=.5, 256^3 DNS)

Magnetic field (top), normalised effective magnetic pressure(middle) and relative density change (bottom) in a plane perpendicular to the applied field
(512^2 Mean-field)