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Nonlinear Propagating Slow Waves in Cooling Coronal Magnetic Loops
We study the propagation of slow magnetosonic waves in coronal magnetic loops. In our
study we take nonlinearity and loop cooling into account. We use the small beta approximation
and neglect the effect of magnetic field perturbation on the wave propagation. In
accordance with this we assume that the tube cross-section does not change. We also neglect
the equilibrium plasma density variation along and across the tube. As a result the
equations of magnetohydrodynamics reduce to purely one-dimensional gasdynamic equations
that includes the effect of viscosity and thermal conduction. We assume that the perturbation
amplitude is sufficiently small and use the reductive perturbation method to derive
the generalised Burgers’ equation describing the evolution of initial perturbations. First we
study a case with weak dissipation and drop the term describing it. When there is no cooling
the evolution of the initial perturbation results in a gradient catastrophe. However strong
cooling can prevent it. Then we solve the full equation numerically assuming that the temperature
decreases exponentially. We fix the initial perturbation amplitude and then study
the dependence of perturbation evolution on the cooling time. The main result that we obtain
is that moderate cooling decelerates the wave damping. This effect is related to the fact
that the dissipation coefficients are proportional to the temperature in 5/2 power. As a result
they decrease fast because of plasma cooling. However strong cooling can cause perturbation
damping on its own.We study the propagation of slow magnetosonic waves in coronal magnetic loops. In our
study we take nonlinearity and loop cooling into account. We use the small beta approximation
and neglect the effect of magnetic field perturbation on the wave propagation. In
accordance with this we assume that the tube cross-section does not change. We also neglect
the equilibrium plasma density variation along and across the tube. As a result the
equations of magnetohydrodynamics reduce to purely one-dimensional gasdynamic equations
that includes the effect of viscosity and thermal conduction. We assume that the perturbation
amplitude is sufficiently small and use the reductive perturbation method to derive
the generalised Burgers’ equation describing the evolution of initial perturbations. First we
study a case with weak dissipation and drop the term describing it. When there is no cooling
the evolution of the initial perturbation results in a gradient catastrophe. However strong
cooling can prevent it. Then we solve the full equation numerically assuming that the temperature
decreases exponentially. We fix the initial perturbation amplitude and then study
the dependence of perturbation evolution on the cooling time. The main result that we obtain
is that moderate cooling decelerates the wave damping. This effect is related to the fact
that the dissipation coefficients are proportional to the temperature in 5/2 power. As a result
they decrease fast because of plasma cooling. However strong cooling can cause perturbation
damping on its own.