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cathode follower asymmetric slew

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What tricks are available, either than replacing tubes, to square a CF's slew rate? My googlefu is failing and the few tricks tried weren't successful.

The background: for fun I designed a headphone amp around a 6FY7. The circuit is ultimate simplicity. The small triode is biased with a pair of IR LEDs cathode to ground getting a further current boost via a 1 meg bleeder to B+, the plate load an IXYS CCS set to around 1.5ma. The small plate is direct coupled to the larger triode, it's plate directly to B+ and another IXYS in the cathode. Op points for the output are roughly 140 Vp and 40 ma Ik. Its output drives an Avel-Lindberg power supply torroid strapped for 230VAC:20VAC, or roughly an 8Kohm primary load driving my 60 ohm headphones.

Though not the ideal choice for a CF the circuit's basic audio performance is spectacular. From memory at an equivalent of roughly 105 dB from my AKGs distortion is ~0.02% 2nd, below 0.005% third and no higher harmonics showing. Midband and down it swings near 20 Vp-p before clip into load and measures otherwise top notch save for slew rate. Pushed to the limits a 10 kHz square wave becomes a saw wave. The waveform at the CF input looks fine and substituting a 10kohm resistor for the CF load does little to improve it. The square wave output is nice, square and clean just below clip from 20 Hz to midband. More plate current helps but the max 50 ma isn't enough.

At the end of the day it still outputs a decent 10 kHz square wave at tinitus inducing levels but any suggestions on taking it to the next level appreciated.
 
Thanks guys. The WCF appears to demand equal currents through both tubes which isn't an option here. Circuit attached below. Slew rates improve rapidly with increased current. The op points shown hit the limit of plate curent while retaining a balance of max output and low distortion.
 

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