The IC origin of TeV emission of SNRs implies the existence of multi-TeV electrons and, therefore, unavoidable synchrotron radiation extending to O/UV and shorter wavelengths. In the galactic plane the magnetic field is estimated to be as large as
Since the the energy density of such magnetic fields exceeds the density of the 2.7 K CMBR (« 4 x 10-13 erg/cm3), the energy flux of TeV radiation is expected to be (always) below the energy flux of synchrotron X-rays. Diffusive shock acceleration models predict significant shock-compression of the magnetic field, by a factor of 4 or even more (in the case of the development of nonlinear shocks). Therefore, the energy flux of TeV emission should not exceed 10 percent of the synchrotron X-ray flux, unless the SNR is located well above the galactic plane and we deal with strictly parallel shock acceleration.
In synchrotron models the spectral fit to the X-ray flux is crucial because the fluxes are produced by electrons in the region of the exponential cutoff E0 between 10 and 100 TeV. For a "power-law with exponential cutoff" type spectra, the power-law index of electrons r is derived from the radio data, while the information about the cutoff energy E0 is contained in the X-ray part of the spectrum. In the particular case of negligible energy losses, the spectrum of electrons N(Ee) repeats the injection spectrum,
therefore in the ^-functional approximation, the differential synchrotron spectrum can be presented in a convenient form
where
is the characteristic synchrotron energy for an electron of energy E0, and q is a free parameter introduced to adapt this formula to accurate numerical calculations, which show that the best broad-band fit with an accuracy of better than 25% in the cutoff region up to e ~ 20e0, is provided by q = 1.
In the framework of diffusive shock acceleration model, the synchrotron cutoff energy is determined by the "acceleration rate=synchrotron loss rate " condition. The acceleration time (see e.g. Malkov and Drury, 2001) can be written, with accuracy of about 50 per cent, in a simple form tacc « 10D/v2 where D is the diffusion coefficient in the upstream region, and v is the upstream velocity into the shock. The diffusion coefficient is generally highly unknown parameter, however if one requires acceleration of electrons to highest energies (thus allowing extension of synchrotron radiation to the X-ray domain), we must assume that the diffusion proceeds in the Bohm regime. Therefore it is convenient to parametrise the diffusion coefficient in terms of the Bohm diffusion coefficient
where
is the particle gyroradius, and
is the gyrofactor; n = 1 implies the smallest possible diffusion coefficient, and correspondingly the shortest possible acceleration time,
The maximum energy of accelerated electrons in the regime dominated by synchrotron losses, is determined from Eqs.(5.8) and (5.12):
From Eqs.(5.10) and (5.13) one can find that the the energy of exponential cutoff in the synchrotron spectrum,
does not depend on either the magnetic field or the age of the source. Since 
and the shock speed in the Sedov phase does not significantly exceed 2000 km/s, the steep featureless X-ray spectrum above 1 keV may serve as a decisive diagnostic tool to identify the synchrotron origin of radiation. On the other hand, the sheer fact of the detection of nonthermal X-radiation from several shell type SNRs (Petre et al., 1999) and its possible synchrotron origin imply that the acceleration of electrons in these SNR proceeds in the regime close to the Bohm diffusion.
