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Thanks for spotting the error. Betza notation was originally designed for indicating moves; (i.e. where a piece can end up relative to its current location), and not for specifying side effects. I admit that the XBetza extension breaks that rule by introducing the 'e' modifier for indicating e.p. capture. And the 'a' modifier for describing what are basically multiple moves per turn can in theory be used to describe side-effect captures, by having the piece jump around before it finally settles on its destination, trampling everything that should disappear first. In the case of the Fire Demon this could be done by having it encircle its final destination with steps that have mpc mode, except that this would make the capture optional, as the 'p' part allows you to jump over the opponent as well. In XBoard I solved this by an ad-hoc extension: 't' in a non-final leg ('tame') there limits any hopping to friendly pieces only. (In final legs I use it to specify a move cannot capture royalty.) So the mode mtpc would do it, and make the Fire Demon's move something like

gyafmtpcabrmtpcafmtpcarmtpcafmtpcarmtpcafmtpcarmtpcarB

and similar things for the vR and aaK components. (The 'gy' in the first leg changes the range from slider to leaper for the subsequent leg(s).) This does not seem really helpful as explanation, however, and the 'a' operator was never meant to be abused for this purpose. (And note that the interactive diagram currently cannot handle more than a single side-effect capture.) It would also not work at the edge of the board, because the FD would not be able to complete the detour there without falling off. This could again be solved by assigning a new meaning for the modifier 'o' in non-final legs, for legs that can step off the board. All intermediate legs should then have the mode mtpooc.

To be of any practical use, a notation would have to be far simpler. I have been playing with the idea to introduce a modifier for 'explosion', (say 'xx') indicating mandatory removal of all adjacent enemy pieces in combination with the mentioned ordinary modes. That would give move components like xxmcB for the FD, which is a lot clearer, and more in line with the philosophy of Betza notation. (I already used a single 'x' for another purpose in the diagram, namely move relay.) Captures of Atomic Chess could then be xxmcdN, etc., the extra 'd' (''destroy') indicating it also works for friendly pieces.

The problem is that this still doesn't give a complete description of the Tenjiku Shogi Fire Demon, as the latter also has passive burning ability, during the opponent's turn, which actually dominates the active ability. So the burning is actually more like a special game rule than a move description; every turn ends with removing your own pieces adjacent to an enemy Demon, and after that removing the enemy pieces adjacent to your own Demons, irrespective of whether the Demons moved or not. That would decouple the burning from the move.