All current flows are accompanied by magnetic fields, AC is not necessary. With AC careful attention to pairing of conductors can lower the extended AC field to very near zero. Such paired, counter directional coils could be compared with non-pair wound coils, if it were thought to be necessary to learn of any magnetic field effects.
Keep in mind that translation from Russian may have lost some subtlety in meaning. Further, Parkhomov may have meant that there was no particular effort to induce a magnetic field, but on reflection or inquiry he may have realized that at least there is the AC field from the heater coils.
whether you are using Dimmer or variac you need AC current. this have no relation to the reaction.
As fas as I have heard, [lexicon]Alexander Parkhomov[/lexicon] is an expermenter with short budget, and he have only observed indication it works...
There is no defintive evidence, and he agree it need to be improved.
Now he have good contact with Russian scientists who will help him.
There is hope his kit chen can be freed from cold fusion experiments. 
See the discussion here on the LENR Forum at "Technical Discussion with [lexicon]Alexander Parkhomov[/lexicon] on his Replications". Clearly dimmers do make a difference. There are at least three functional types of dimmers currently on the market (leading edge and trailing edge "choppers", as well as asynchronous types.. All are capable of producing switching noise harmonics--- apparently thought by at least a few to be essential to the Rossi or Lugano or Parkhomov "effects".
It seems plausible, but is this really so? It seems to be a rather arbitrary and likely low powered source of "stimulus" for LENR. If it really is important, who is experimenting with the power levels, the frequencies, the phase relationships or lack thereof?
It appears that often too few "endpoints" are being examined-- perhaps for lack of instrumentation, but also an apparent lack of good "reduction of theory to practice".
