INDUSTRIAL ELECTROHEATING AND ELECTROMAGNETIC PROCESSING EQUIPMENT –
H.5 The frequency upscaling procedures
As described in I EEE C95. 3. 1 -201 0, section 7. 2, frequency upscaling is necessary for low frequencies when using numerical FDTD m odelling m ethods. These suffer from the need to com pl y with a stability criterion which requires short tim esteps which at some hundred kH z typicall y becom e impracticall y m an y per cycle with regard to CPU tim e. The number of tim esteps per cycle needed for stationary conditions to be created is inversel y proportional to the frequency, and the sm allest necessary voxel sizes of som e few millimetres are independent of the frequency.
FDTD m ethods typicall y have an important advantage over finite elem ent (FEM) methods in the d ynamic range of field am plitudes. Such large d ynam ic ranges are needed with modelling of e. g. induction system s and with other scenarios with a very large range of field amplitudes.
The B field can be very strong in the workload treatm ent section and decays very quickl y as a nearfield away from that section. Additionall y, very low induced E field and SAR are allowed in hum an bod yparts in comparison with the process data in the workload. Modern comm erciall y available FDTD software contains advanced ABC (absorbing boundary condition) options suitable also for scenarios with sizes much smaller than a free space wavelength. H owever, accurate sim ulation of free space conditions around in particular the excitation regions in practice require additional circumferential absorbing means; see Clauses E. 1 and H. 1 .
The basic frequency scaling factor results in the induced E field amplitude at constant B amplitude (and thus constant source current) being proportional to the frequency. The obtained E value is divided by the fhi gh / flow factor in the recalculations after the modelling.
The bod y tissue conductivity is frequency dependent and the quotient between that at flow and the value used in the m odelling at fhig h is also to be used in the recalculation when the SAR is sought for.
H.5.2 Choices of condu ctivity and control procedures
The conditions of Formulas (H. 5) and (H .7) are adhered to in the selection of the upscaled frequency in FDTD m odelling. Since they are contradictory, an interactive procedure is normall y applied. The typical procedure is to firstl y use the actual conductivity values at the prelim inary upscaled frequency, for checking with Form ula (H. 7); the value should preferabl y be > 1 000 Sm-1 for the lowest conductivity. The highest conductivity is then tested with Form ula (H .5); if the combined parts of the body now all with that conductivity are < 2 dp no changes of an y conductivity is needed at the upscaled frequency.
Conductivities of all parts of the bod y are to be increased with an equal factor if Formula (H. 6) is not fulfilled.
I f Formula (H. 5) is not fulfilled or when the condition in Formula (H. 6) is needed for separation of the capacitively induced power deposition pattern, the first alternati ve is to run the scenario an yway, to see which parts of the bod y get the highest E value.
A second m ethod is to run a Helm holtz coil scenario with the possibly too high conductivities and look at the B field (stationary or at its second maxim um in time); if this is constant over the whole set of bod yparts, Formula (H . 5) is fulfilled.
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