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An oscillating combustor may support a time-sequenced combustion reaction having rich and lean phases. The rich and lean phases may be determined according to a flame position relative to a diverging fuel jet. The flame location may be modulated responsive to an interaction between applying a consta

An oscillating combustor may support a time-sequenced combustion reaction having rich and lean phases. The rich and lean phases may be determined according to a flame position relative to a diverging fuel jet. The flame location may be modulated responsive to an interaction between applying a constant voltage or charge rate to a fuel stream or flame, and modulating continuity between a conductive or semiconductive flame holder and an activation voltage.

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1. An oscillating combustor, comprising: a fuel nozzle configured to emit an expanding area fuel jet;a first flame holder disposed distally along the fuel jet;a second flame holder disposed proximally along the fuel jet;an ionizer configured to apply a charge to the fuel jet or a flame supported by

1. An oscillating combustor, comprising: a fuel nozzle configured to emit an expanding area fuel jet;a first flame holder disposed distally along the fuel jet;a second flame holder disposed proximally along the fuel jet;an ionizer configured to apply a charge to the fuel jet or a flame supported by the fuel jet; anda continuity modulator operatively coupled to the second flame holder and configured to modulate continuity between the second flame holder and an activation voltage, wherein the continuity modulator is configured to make electrical continuity between the activation voltage and the second flame holder to cause the combustion reaction to be held by the second flame holder, and to break the electrical continuity between the activation voltage and the second flame holder to cause the combustion reaction to be held by the first flame holder. 2. The oscillating combustor of claim 1, wherein the fuel nozzle is configured to emit a substantially constant flow rate fuel jet. 3. The oscillating combustor of claim 1, wherein the fuel nozzle is configured to emit a variable flow rate fuel jet. 4. The oscillating combustor of claim 3, wherein the nozzle is configured to emit a variable flow rate fuel jet that is synchronized with the modulation of electrical continuity to the second flame holder. 5. The oscillating combustor of claim 4, wherein the synchronization includes a phase relationship between the fuel flow rate variation and the modulation. 6. The oscillating combustor of claim 1, wherein the activation voltage consists essentially of a voltage ground. 7. The oscillating combustor of claim 1, wherein the ionizer is configured to apply a first polarity charge to the fuel jet or flame; and wherein the activation voltage consists essentially of a voltage opposite in polarity to the first polarity. 8. The oscillating combustor of claim 1, wherein the ionizer is configured to apply electrical charge to the fuel jet or flame supported by the fuel jet at a sufficiently high rate to cause the flame to carry a high voltage. 9. The oscillating combustor of claim 1, wherein the ionizer is configured to cause the flame to carry a voltage of magnitude about 10 kilovolts or more. 10. The oscillating combustor of claim 1, wherein second flame holder is conductive. 11. The oscillating combustor of claim 1, wherein the second flame holder is formed from a semiconductor. 12. The oscillating combustor of claim 1, wherein the continuity modulator is configured to cause the flame to oscillate between a position near the first flame holder and a position near the second flame holder. 13. The oscillating combustor of claim 1, wherein the continuity modulator is configured to cause the flame to oscillate in position between the first and second flame holders corresponding to oscillation between a lean mixture and a rich mixture, respectively. 14. The oscillating combustor of claim 13, wherein the rich mixture includes a time-averaged oxidizer concentration near a rich flammability limit of the fuel. 15. The oscillating combustor of claim 13, wherein the lean mixture includes a time-averaged oxidizer concentration near a lean flammability limit of the fuel. 16. The oscillating combustor of claim 1, wherein the continuity modulator includes an insulated gate bipolar transistor (IGBT). 17. The oscillating combustor of claim 1, wherein the oscillating combustor is configured to combust a time-series of rich and lean combustion packets. 18. The oscillating combustor of claim 17, wherein the rich combustion packets have about half the amount of oxygen required for stoichiometric combustion. 19. The oscillating combustor of claim 17, wherein the lean combustion packets have about 1.3 to 1.5 times the amount of oxygen required for stoichiometric combustion. 20. The oscillating combustor of claim 1, wherein the continuity modulator is configured to cause oscillation of the position of the flame at a frequency of between 0.5 and 15 Hertz.