This is an LTSpice model of Tim William's circuit, changed more or less as John Larkin suggested. It costs a few extra components to keep it stable and stop it feeding current spikes back into the 9V supply, but fewer than are needed to keep Tim's original circuit tidy - see my recent postings to that thread.
The ferrite beads L9 and L10 stop the high voltage output rectifier from messing up the inverter, and let it run at 135kHz.
Version 4 SHEET 1 1296 836 WIRE -1184 -720 -1232 -720 WIRE -880 -720 -1120 -720 WIRE -304 -720 -880 -720 WIRE -48 -720 -304 -720 WIRE 112 -720 -48 -720 WIRE -880 -688 -880 -720 WIRE 112 -688 112 -720 WIRE -304 -672 -304 -720 WIRE -304 -432 -304 -592 WIRE -48 -432 -48 -720 WIRE -880 -384 -880 -608 WIRE -368 -384 -880 -384 WIRE 896 -272 864 -272 WIRE 976 -272 960 -272 WIRE 1072 -272 976 -272 WIRE 1200 -272 1072 -272 WIRE -304 -256 -304 -336 WIRE -304 -256 -448 -256 WIRE -208 -256 -304 -256 WIRE 16 -256 -128 -256 WIRE 176 -256 16 -256 WIRE 368 -256 176 -256 WIRE 16 -224 16 -256 WIRE 176 -208 176 -256 WIRE 368 -208 368 -256 WIRE 864 -192 864 -272 WIRE 1200 -176 1200 -272 WIRE 976 -144 976 -272 WIRE 16 -128 16 -160 WIRE 112 -128 112 -624 WIRE 112 -128 16 -128 WIRE 176 -128 176 -144 WIRE 176 -128 112 -128 WIRE 368 -112 368 -144 WIRE 176 -96 176 -128 WIRE -448 -80 -448 -256 WIRE 864 -80 864 -128 WIRE 224 16 64 16 WIRE 448 16 224 16 WIRE 784 16 624 16 WIRE 864 16 864 -16 WIRE 864 16 784 16 WIRE 448 32 448 16 WIRE 64 48 64 16 WIRE 624 80 624 16 WIRE 784 80 784 16 WIRE -448 96 -448 0 WIRE 0 96 -160 96 WIRE 224 112 224 16 WIRE -160 128 -160 96 WIRE -1232 144 -1232 -720 WIRE 368 144 368 -32 WIRE 448 144 448 112 WIRE 448 144 368 144 WIRE 1072 144 1072 -272 WIRE 448 176 448 144 WIRE -160 240 -160 208 WIRE -48 240 -48 -352 WIRE -48 240 -160 240 WIRE -160 272 -160 240 WIRE 624 272 624 160 WIRE 784 272 784 144 WIRE 784 272 624 272 WIRE 976 272 976 -80 WIRE 976 272 784 272 WIRE 992 272 976 272 WIRE 224 288 224 176 WIRE 448 288 448 256 WIRE 448 288 224 288 WIRE 864 288 864 16 WIRE 224 320 224 288 WIRE 992 352 992 272 WIRE -160 368 -160 352 WIRE 160 368 -160 368 WIRE 864 384 864 352 WIRE 1200 400 1200 -96 WIRE 64 448 64 144 WIRE 224 448 224 416 WIRE 224 448 64 448 WIRE -880 496 -880 -384 WIRE -832 496 -880 496 WIRE -448 496 -448 160 WIRE -448 496 -576 496 WIRE -352 496 -448 496 WIRE -208 496 -352 496 WIRE 1200 496 1200 480 WIRE 1200 496 -144 496 WIRE 1200 528 1200 496 WIRE 864 560 864 448 WIRE -352 576 -352 496 WIRE -880 624 -880 496 WIRE -832 624 -880 624 WIRE -544 624 -576 624 WIRE -48 624 -48 240 WIRE 1200 640 1200 608 WIRE -544 688 -544 624 WIRE -544 688 -576 688 WIRE -1232 768 -1232 224 WIRE -544 768 -544 688 WIRE -544 768 -1232 768 WIRE -352 768 -352 640 WIRE -352 768 -544 768 WIRE -48 768 -48 704 WIRE -48 768 -352 768 WIRE 224 768 224 448 WIRE 224 768 -48 768 WIRE 784 768 224 768 WIRE 864 768 864 624 WIRE 864 768 784 768 WIRE 992 768 992 416 WIRE 992 768 864 768 WIRE 1072 768 1072 208 WIRE 1072 768 992 768 WIRE 1200 768 1200 720 WIRE 1200 768 1072 768 WIRE 784 816 784 768 FLAG 784 816 0 FLAG 176 -96 0 SYMBOL npn 160 320 R0 SYMATTR InstName Q1 SYMATTR Value 2N4401 SYMBOL npn 0 48 R0 SYMATTR InstName Q2 SYMATTR Value 2N4401 SYMBOL ind2 432 16 R0 SYMATTR InstName L1 SYMATTR Value 44µ SYMATTR Type ind SYMATTR SpiceLine Rser=0.1 Cpar=1p SYMBOL ind2 432 160 R0 SYMATTR InstName L2 SYMATTR Value 44µ SYMATTR Type ind SYMATTR SpiceLine Rser=0.1 Cpar=1p SYMBOL cap 208 112 R0 SYMATTR InstName C1 SYMATTR Value 2.2n SYMBOL ind2 608 64 R0 SYMATTR InstName L5 SYMATTR Value 4.4m SYMATTR Type ind SYMATTR SpiceLine Rser=0.1 Cpar=1p SYMBOL cap 768 80 R0 SYMATTR InstName C2 SYMATTR Value 220p SYMBOL diode 880 -16 R180 WINDOW 0 24 64 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName D1 SYMATTR Value 1N914 SYMBOL diode 880 -128 R180 WINDOW 0 24 64 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName D2 SYMATTR Value 1N914 SYMBOL diode 880 352 R180 WINDOW 0 24 64 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName D3 SYMATTR Value 1N914 SYMBOL diode 880 448 R180 WINDOW 0 24 64 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName D4 SYMATTR Value 1N914 SYMBOL cap 960 -144 R0 SYMATTR InstName C3 SYMATTR Value 6.8n SYMBOL cap 976 352 R0 SYMATTR InstName C4 SYMATTR Value 6.8n SYMBOL cap 1056 144 R0 SYMATTR InstName C5 SYMATTR Value 100n SYMBOL res 1184 -192 R0 SYMATTR InstName R1 SYMATTR Value 1000k SYMBOL res 1184 384 R0 SYMATTR InstName P1a SYMATTR Value 5k SYMBOL res 1184 512 R0 SYMATTR InstName P1b SYMATTR Value 5k SYMBOL res 1184 624 R0 SYMATTR InstName R4 SYMATTR Value 15k SYMBOL ind2 -144 224 R180 WINDOW 0 36 80 Left 2 WINDOW 3 36 40 Left 2 SYMATTR InstName L3 SYMATTR Value 4µ SYMATTR Type ind SYMATTR SpiceLine Rser=0.1 Cpar=1p SYMBOL ind2 -144 368 R180 WINDOW 0 36 80 Left 2 WINDOW 3 36 40 Left 2 SYMATTR InstName L4 SYMATTR Value 4µ SYMATTR Type ind SYMATTR SpiceLine Rser=0.1 Cpar=1p SYMBOL ind 352 -128 R0 SYMATTR InstName L6 SYMATTR Value 270µ SYMATTR SpiceLine Rser=1 Cpar=1p SYMBOL polcap 160 -208 R0 WINDOW 3 24 56 Left 2 SYMATTR Value 47µ SYMATTR InstName C6 SYMATTR Description Capacitor SYMATTR Type cap SYMATTR SpiceLine V=4 Irms=0 Rser=2.4 Lser=0 mfg="AVX" pn="TAJB476M004" type="Tantalum" SYMBOL References\\LT1431 -704 592 R0 SYMATTR InstName U1 SYMBOL res -64 -448 R0 SYMATTR InstName R2 SYMATTR Value 6.8k SYMBOL res -64 608 R0 SYMATTR InstName R3 SYMATTR Value 680 SYMBOL voltage -1232 128 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value 9 SYMBOL FerriteBead -1152 -720 R90 WINDOW 0 -16 0 VBottom 2 SYMATTR InstName L7 SYMATTR Value 3.642µ SYMATTR SpiceLine Ipk=0.2 Rser=0.6 Rpar=2700 Cpar=1.122p mfg="Wurth Elektronik" pn="742 792 092" SYMBOL FerriteBead 368 -176 R180 SYMATTR InstName L8 SYMATTR Value 3.642µ SYMATTR SpiceLine Ipk=0.2 Rser=0.6 Rpar=2700 Cpar=1.122p mfg="Wurth Elektronik" pn="742 792 092" SYMBOL npn -368 -432 R0 SYMATTR InstName Q3 SYMATTR Value 2N4401 SYMBOL FerriteBead 928 -272 R90 WINDOW 0 -16 0 VBottom 2 SYMATTR InstName L9 SYMATTR Value 3.642µ SYMATTR SpiceLine Ipk=0.2 Rser=0.6 Rpar=2700 Cpar=1.122p mfg="Wurth Elektronik" pn="742 792 092" SYMBOL FerriteBead 864 592 R180 SYMATTR InstName L10 SYMATTR Value 3.642µ SYMATTR SpiceLine Ipk=0.2 Rser=0.6 Rpar=2700 Cpar=1.122p mfg="Wurth Elektronik" pn="742 792 092" SYMBOL res -464 -96 R0 SYMATTR InstName R7 SYMATTR Value 47k SYMBOL cap -464 96 R0 SYMATTR InstName C7 SYMATTR Value 10n SYMBOL res -896 -704 R0 SYMATTR InstName R5 SYMATTR Value 1k SYMBOL res -320 -688 R0 SYMATTR InstName R6 SYMATTR Value 100 SYMBOL FerriteBead -176 496 R90 WINDOW 0 -16 0 VBottom 2 SYMATTR InstName L11 SYMATTR Value 3.642µ SYMATTR SpiceLine Ipk=0.2 Rser=0.6 Rpar=2700 Cpar=1.122p mfg="Wurth Elektronik" pn="742 792 092" SYMBOL cap -368 576 R0 SYMATTR InstName C8 SYMATTR Value 22n SYMBOL cap 0 -224 R0 SYMATTR InstName C9 SYMATTR Value 100n SYMBOL cap 96 -688 R0 SYMATTR InstName C10 SYMATTR Value 100n SYMBOL ind -112 -272 R90 WINDOW 0 5 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName L13 SYMATTR Value 4.7m SYMATTR SpiceLine Rser=13.8 Cpar=5p TEXT 368 352 Left 2 !K1 L1 L2 L3 L4 L5 0.999 TEXT 552 104 Left 2 ;| TEXT 552 128 Left 2 ;| TEXT 536 104 Left 2 ;| TEXT 536 128 Left 2 ;| TEXT -728 816 Left 2 !.tran 0 50m 0 10n startup TEXT -208 -192 Left 2 ;Multicomp TEXT -232 -160 Left 2 ;MCSD75_472KU TEXT -224 -128 Left 2 ;Farnell 1864155