We review recent developments of amplification models of galactic and intergalactic magnetic field. The most popular scenarios involve variety of physical mechanisms, including turbulence generation on a wide range of physical scales, effects of supernovae, buoyancy as well as the magnetorotational instability. Other models rely on galaxy interaction, which generate galactic and intergalactic magnetic fields during galaxy mergers. We present also global galactic-scale numerical models of the Cosmic Ray (CR) driven dynamo, which was originally proposed by Parker (1992). We conduct a series of direct CR+MHD numerical simulations of the dynamics of the interstellar medium (ISM), composed of gas, magnetic fields and CR components. We take into account CRs accelerated in randomly distributed supernova (SN) remnants, and assume that SNe deposit small-scale, randomly oriented, dipolar magnetic fields into the ISM. The amplification timescale of the large-scale magnetic field resulting from the CR-driven dynamo is comparable to the galactic rotation period. The process efficiently converts small-scale magnetic fields of SN-remnants into galactic-scale magnetic fields. The resulting magnetic field structure resembles the X-shaped magnetic fields observed in edge-on galaxies.

We present a new multi–fluid, grid MHD code PIERNIK, which is based on the Relaxing TVD scheme (Jin & Xin 1995). The original scheme (see Trac & Pen 2003; Pen 2003) has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing–box boundary conditions, and a selfgravity module, Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid–dynamical simulations. The code is parallelized by means of the MPI library. In this paper we present an extension of PIERNIK, which is designed for simulations of diffusive propagation of the Cosmic–Ray (CR) component in the magnetized ISM.

We present new developments on the cosmic-ray driven, galactic dynamo, modeled by means of direct, resistive CR–MHD simulations, performed with ZEUS and PIERNIK codes. The dynamo action, leading to the amplification of large–scale galactic magnetic-fields on galactic rotation timescales, appears as a result of galactic differential rotation, buoyancy of the cosmic-ray component and resistive dissipation of small–scale turbulent magnetic-fields. Our new results include demonstration of the global–galactic dynamo action driven by cosmic-rays supplied in supernova remnants. An essential outcome of the new series of global galactic dynamo models is the equipartition of the gas turbulent energy with magnetic-field energy and cosmic-ray energy, in saturated states of the dynamo on large galactic scales.

We present a new multi–fluid, grid MHD code PIERNIK, which is based on the Relaxing TVD scheme (Jin & Xin 1995). The original scheme (see Trac & Pen 2003; Pen et al 2003) has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing–box boundary conditions, and a selfgravity module, Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid–dynamical simulations. The code is parallelized by means of the MPI library. In this paper we present Ohmic resistivity extension of the original Relaxing TVD MHD scheme, and show examples of magnetic reconnection in cases of uniform and current–dependent resistivity prescriptions.

We study the global evolution of the magnetic field and interstellar medium (ISM) of the barred and ringed galaxies in the presence of non-axisymmetric components of the potential, i.e. the bar and/or the oval perturbations. The magnetohydrodynamical dynamo is driven by cosmic rays (CR), which are continuously supplied to the disk by supernova (SN) remnants. Additionally, weak, dipolar and randomly oriented magnetic field is injected to the galactic disk during SN explosions. To compare our results directly with the observed properties of galaxies we construct realistic maps of high-frequency polarized radio emission. The main result is that CR driven dynamo can amplify weak magnetic fields up to few μG within few Gyr in barred and ringed galaxies. What is more, the modelled magnetic field configuration resembles maps of the polarized intensity observed in barred and ringed galaxies.

We present recent developments of global galactic-scale numerical models of the Cosmic Ray (CR) driven dynamo, which was originally proposed by Parker (1992). We conduct a series of direct CR+MHD numerical simulations of the dynamics of the interstellar medium (ISM), composed of gas, magnetic fields and CR components. We take into account CRs accelerated in randomly distributed supernova (SN) remnants, and assume that SNe deposit small-scale, randomly oriented, dipolar magnetic fields into the ISM. The amplification timescale of the large-scale magnetic field resulting from the CR-driven dynamo is comparable to the galactic rotation period. The process efficiently converts small-scale magnetic fields of SN-remnants into galactic-scale magnetic fields. The resulting magnetic field structure resembles the X-shaped magnetic fields observed in edge-on galaxies.

We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on theRelaxing Total Variation Diminishing (RTVD) scheme (Jin & Xin 1995). The original scheme (see Trac & Pen 2003 and Pen et al.  2003) has been extended by an addition ofdynamically independent, but interacting fluids: dust and a diffusive cosmic ray (CR)gas, described within the fluid approximation, with an option to add otherfluids in an easy way. The code has been equipped with shearing-box boundaryconditions, a selfgravity module, an Ohmic resistivity module, as well as otherfacilities which are useful in astrophysical fluid-dynamical simulations. Thecode is parallelized by means of an MPI library. In this paper weintroduce a multifluid extension of the RTVD scheme and present a test caseof dust migration in a two-fluid disk composed of gas and dust. We demonstratethat due to the difference in azimuthal velocities of gas and dust and the drag force acting on both components, dust drifts towardsmaxima of the gas pressure distribution.

We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on theRelaxing Total Variation Diminishing (RTVD) scheme. The original scheme has been extended by an addition ofdynamically independent, but interacting fluids: dust and a diffusive cosmic ray (CR)gas, described within the fluid approximation, with an option to add otherfluids in an easy way. The code has been equipped with shearing-box boundaryconditions, a selfgravity module, an Ohmic resistivity module, as well as otherfacilities which are useful in astrophysical fluid-dynamical simulations. Thecode is parallelized by means of an MPI library. In this paper we brieflyintroduce the basic elements of the RTVD MHD algorithm, following Trac & Pen (2003) and Pen et al.  (2003), and then focus on a conservativeimplementation of the shearing-box model, constructed with the aid of Masset's (2000) method. We present the results of a test example of the formation of a gravitationally bound object (a planet) in a self-gravitating and differentially rotating fluid.

We present new developments on the Cosmic–Ray driven, galactic dynamo, modeled by means of direct, resistive CR–MHD simulations, performed with ZEUS and PIERNIK codes. The dynamo action, leading to the amplification of large–scale galactic magnetic fields on galactic rotation timescales, appears as a result of galactic differential rotation, buoyancy of the cosmic ray component and resistive dissipation of small–scale turbulent magnetic fields. Our new results include demonstration of the global–galactic dynamo action driven by Cosmic Rays supplied in supernova remnants. An essential outcome of the new series of global galactic dynamo models is the equipartition of the gas turbulent energy with magnetic field energy and cosmic ray energy, in saturated states of the dynamo on large galactic scales.

We describe the basic process of coupling between dynamo and density waves in galaxies. The growth rate of magnetic field as a result of coupling is derived, applying the method of multiple time scales to the marginal state of disk dynamo. It is shown that the 1st-order resonance in a perturbation of density and thus the linear swing excitation, is possible. Moreover, the growth rate of magnetic field is always positive and does not depend on the initial phase difference between the magnetic and density waves. Both the numerical and analytical calculations show that ω = 2ω0 (ω: density-wave freq., ω0: dynamo freq.) is still the best condition for resonance due to the linear effect of swing excitation.

We imagine the interstellar medium as a system of molecular clouds and isolated magnetic flux tubes. We assume that: the flux tubes appear as a result of disruption of molecular clouds containing magnetic field, their length is comparable to the mean intercloud distance of about 100 pc and diameter comparable to the diameter of the clouds ∼ 10 pc.