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The Cheetah Light has to be in H mode for power levels below full power. That activates the rapid cycling that creates a flat power level for the time it takes the shutter slit to travel across the sensor. To make that happen, the camera sends an FP-sync pulse to fire the flash just a bit before the shutter travel starts so the light will be on when it starts.
In order to get the camera to recognize the FP-sync one has to have a device attached to the hot shoe that the camera thinks is a HSS enabled speedlites. The ControlTL triggers (FlexTT5 or MiniTT1), the Yongnou YN-622 and the the Cells II trigger available from Cheetah has the required pins and firmware to make this happen. There may be others but those are the only ones I have either used or seen specific examples from. I have also seen examples of the ControlTL Nikon devices working to support H mode.
As with a speedlite, the need for the capacitor energy to fire the flash tube rapidly for the duration of the shutter travel means that less illuminate will be striking the sensor through the slit as it travels. With the Cheetah Light it remains consistent at about 1EV less than an equivalent power setting using x-sync. i.e. a shutter speed less than x-xync speed on the camera.
Here's an example of how it can be used in bright sun;
The camera was a 5DIII, about 1/4000 shutter, ISO 100, F2.8 about 2:00p CDT in Chicago so the sun was high and bright. The CL-360 was camera right, basically opposite the sun to open up the shadows. The light was at H mode 1/2.