Accelerated heavy ions can interact with the target HTS crystal via elastic collisions with the target atoms or via inelastic interaction with the crystal lattice, resulting in ion-ization or excitation of electron states of the crystal. The type of the incurring damage will depend on the rate of energy loss, dE/dx, of the ions as they penetrate the crystal.
For low-energy ions, elastic collisions dominate, resulting in displacement of atoms from crystal lattice and pointlike defects. For high-energy ions, inelastic collisions dominate. Experiment shows that the inelastic collisions with high-energy ions can result in amorphous columnar tracks in HTSs . The diameter of the tracks is about 10 nm and the length is tens of /m. An important parameter defining the formation of the columnar defects is the electronic energy loss, also called electronic stopping power, Se. It is defined as the energy transfer into the electronic excitations of the target atoms per unit length along the ion path through the target crystal: Se = -dEe/dx. The value of Se depends on the type of the target crystal, type, and energy of the ion and direction of the irradiation in regard to the crystal structure. It can be approximated as 
where Z and Zi are respectively the atomic numbers of the incident ions and various target atoms, E is the energy of incident ions, n is the number of the target atoms of type i per unit volume, M and me are respectively the mass of the incident ion and electron, h is the Planck constant, and e is the base of natural logarithms.
Formation of amorphous columnar defects is described by the thermal spike model [69-72]. Because columnar defects are formed as a consequence of electronic excitation by the heavy ions, there has to be a mechanism of the transfer of this energy to the crystal lattice. The thermal spike model does not explain the nature of these interactions; however, it explains formation of the columnar defects in a thermo-dynamic approach. The energy transfer from the heavy ions to the electronic excitations occurs on a much smaller time scale than the subsequent transfer of this energy into the thermal energy of the crystal lattice. This heats up the crystal on a very localized scale around the atom targeted by a heavy ion. The heat is then diffused to the rest of the crystal on a larger time scale than the energy transfer to the crystal lattice, until the thermal equilibrium is reached.
Because of the transfer of the energy from the heavy ions to the electrons and to crystal lattice on a subsequently increasing time scale, a sudden localized increase of temperature occurs around the target atom of the crystal. For the value of Se higher than a threshold value Se0, the crystal lattice melts in much localized volume along the ion track. Because the diameter of the molten volume is very small (of the order of a nanometer), this heat is diffused through the crystal lattice quickly enough to freeze the molten volume without allowing recrystallization. Consequently, a track of amorphous material is formed in the crystal, which is not superconducting.
High-resolution electron microscopy analysis suggests that there are five ranges with different types of the damage, depending on Se [67, 73-75]. Below Se0, the damage occurs only due to the elastic collisions. For higher values of Se, small spherical amorphous defects were observed along the ion track. These defects become elongated for yet higher Se. For still higher Se, discontinuous amorphous cylinders were observed along the ion track. For the largest values of Se, continuous columnar amorphous cylinders were observed along the whole of the ion tracks. The values of Se separating different ranges depend on the properties of the ions and target.
The thermal spike model gives a relationship between Se and the track diameter. For the ion beam directed along the c-axis of the crystal, the amorphous track is of circular cross-section with diameter 
where C is the heat capacity per unit volume and ATm is the difference between the melting and ambient temperature when the ion travels along the a- or fo-axis of the crystal. If the ion travels along the a- or fo-axis, the amorphous track is
mwe of elliptical cross-section. The elliptical axes in the afo-plane and c-axis are respectively 
Here, Dab = o-ab/C and Dc = ac/C, with aab and ac being the thermal conductivity in the crystalline afo-plane and along the c-axis, respectively. The value of d increases with the energy of the heavy ions via Se and ATm in Eq. (7).
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