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Description
Transcript
イオントラップを駆動するための高電圧矩形波発生器
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............................................................................................. 3
2N
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2.1 RF ................................................................................. 5
2.2
.................................................................. 10
2.2.1 &_*.................................... 11
2.3
%i)Z9' .................................................................................... 14
2.3.1
Dc/`K;B............................................................. 15
2.3.2 AM 2WJ;B .................................................................... 18
3N
hc/M7CLI- ......................................................................... 22
3.1
@U .................................................................................................. 22
3.2 MOSFET Jh^.[ ........................................... 26
3.2.1 MOSFET Jh^ ................................................... 26
3.2.2 "]P[........................................................................... 28
3.3 h^$A.[ ........................................................................................ 30
3.3.1 fS<b0Ya(>VFJ ... 30
3.3.2 h^$A.[ .................................................................................. 30
3.4 AM 2W.[ ........................................................................................ 32
4N
5g .................................................................................................. 35
4.1
5gTQ ........................................................................................... 35
4.2
5gj 34e1 .................................. 37
E48d5g=!................................................................................... 37
O?R6 ................................................................................................. 39
4.3
5gk %i)Z9'...................................................................... 40
4.3.1
Dc/`K;B............................................................. 40
E48d5g=!................................................................................... 40
E4O?R6 .......................................................................................... 40
4.3.2 AM 2WJ;B .................................................................... 44
E48d5g=!................................................................................... 44
E4O?R6 .......................................................................................... 44
............................................................................................................... 48
X\ .................................................................................................................. 49
,R:G ........................................................................................................... 50
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2 %;0'4,1_ + V0 / 2 8;(_ V0 / 2 R#JG!
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5
U(r,z) =
V0 2
(r 2z 2 ) 2r02
(2.3)
V0 -,3&'#!(% 2.2 .5 V0 -,3&'#
!(% 2.2 .5'# r )$2/
"4 z )$0
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5
% 2.1 RF 3*+15
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RP^@ VDC :7_',%)5*&/$+._D(2.3) V0 VAC cost + VDC UI_
U(r,z) =
VAC cost + VDC 2
(r 2z 2 )
2
2r0
(2.4)
`',%)0Z\ m _^V e !/[8LTD r _ z L>
d 2 r VAC cost + VDC e
r=0
2+
dt
m
r02
2
d z 2 VAC cost + VDC e z = 0
dt 2
m
r02
(2.5)
`OUIW`
t
=
2
8eVDC
a z = 2a r = 2 2
mr0 4eVAC
q z = 2q r =
mr02 2
(2.6)
D(2.5)Da[8LTD=FX_
d 2u
+ (ai 2qi cos 2 )u = 0 (u = r , z )
d 2
7
(2.7)
X(2.7) Mathieu ]nXKtuta
[5]
Mathieu ]nX=qtbX?
(2.8)
u( ) = A C2n cos(2n + i ) + B C2n sin(2n + i ) = 0
n=
n=
A B E_`AeC2n ai qi ~[]nXt ai , qi
L 2.3 m^pDSTL 2.3 STN'(.8+"
<)#!%72K r w]ISTPip r = 0 r = 1 z w]I
STPip z = 0 z = 1YN ai , qi Mathieu -73
<(K
ai , qi 1 OHX(2.8)\gyBtalt
q
u (t ) = A0 1 + i cos t cos si = 0
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si =
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i
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(2.10)
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(2.11)
0+;&49
eff (r,z) =
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( r r + z2 z 2 )
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(2.12)
@r e v| m #$;zFoX(2.9)
zF
sZF[ si QZVZF>}xh RF MsZF[ U
si dWJf[KdWJf[#
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ZFL 2.4 RF #$;,7*/@ 107 Ag + #$;,7*/D
zF&15:<&6;
m#$;,7*/Q
z 0 = 8 mm r0 =
8
11.3 mm &'7+: /2 = 1 MHz:VAC = 200 V: VDC = 0 V::
"1 x, y,z 4)$50 100 m/s 3:!#
-(2/;:qz = 0.143: az = 0: sz /2 =
50.65 kHz: sr /2 = 25.25 kHz ;9
* 2.3 RF ./8,;
* 2.4 RF " 107 Ag + 6%
9
2.2
RF !/(,&*XURJW:H<IW:J
YX45W:@H<I@QX7CKI>
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-/#WE
/)"+&*WEV42Y
X!/(,&
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Y
d 2u
+ ( 0 + 2 n cos2n )u = 0(u = r,z)
d 2
n=1
;(2.13) Hill BN;8Y
9 2.5 '$%.!/(,&*45L>IW:Y
10
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2.2.1 (%&0"#2)/'*;"#2j?oAFGO
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p
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= 11
21
12 (2.15)
22 11,12 ,21,22 o7Y_9bhI+!
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ko t = t 0 + T 9bhI
j?Q^JVoi_Q^J(2.17)
eVp
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11
(2.17)
1 n 2
EW<n t = t 0 + nT !"0:diLZM
5o Q nM(2.19)Keo
n
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u& (t 0 + nT ) u& (t 0 ) 0
0 -1 u (t 0 ) Q (2.18)
n2 u& (t 0 ) 1 0 1
= Q Q (2.19)
0
2
M(2.18)!"0JK(-&)X8n fcg
n74EW<VaM(2.20)M(2.21) ]o
11 21
12
= 2 ( 11 + 22 ) + 1
( 11 22 12 21 = 1) (2.20)
22 (2.21)
11 + 22 < 2
73U<hb
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D 2.6
`o VDC n VAC D 2.5 `Keo ai , qi [N\k
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0
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r
z
mr02 2
_O\kF
(2.22)
^HAn[N\kFHAm9JKlG
ToD 2.7 '$%.!"0(-&)6 107 Ag + j>#*+/1#,0
`o!"0(-&)In z 0 = 8 mmn r0 = 11.3 mm ?@kF
n /2 = 1 MHzn VAC = 200 Vn VDC = 0 Vnn!"0(-&)6Q
x, y,z VC=iL
100 m/s
Sn!"0
2;
(-&)HA
RKonqz = 0.143n az = 0n sz /2 = 50.65 kHzn sr /2 =
12
25.25 kHz 2.6 2.7 107 Ag + 13
2.3
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P-459;-6:
+,:2703_ z 0 = 8 mmr0 = 11.3 mm $|fy
[Wyq /2 450 kHzVAC = 293 VVDC = 0 V 2703?i
& x, y,z rV)) 0.1 mm )\ke* 100 m/s n107 Ag 2 79 Br + <F2703)(\T*ja0.1 ms 2703g))
IOpK|[*(qz =
0.377az = 0 z /2 = 80.46
kHz r /2 = 38.77 kHz ())IOpK|[G
-459;-6:%' Ag2Br UDEL`*))<
IOp
K([G
IOpK|[(Wyq[*Io+,
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rV))0.1 m)\ke*100 m/sn`
<F2703
14
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V = Vrec + VS cos pt
p Vrec ZKTlBp Vs p p !!gY
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nAG^ieWZKTlBpV^gY
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15
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.J;,DT
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16
960/8'
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& 2.9 1).8'/8'60
!
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17
2.3.2 AM 4a7ZH6O`?d_[ORFL`?AM@X!b>
2.11ce
:;`?20Ve
(2.23)
V = (1+ ma cos pt)Vrec
dVrec RFL`?dma dp @XD@XLWG8Ie
> 2.11 RFL`? AM @X!LFe
b>BU_[ORFL`?dNU AM L9TUd ma @XDec
AM @XL=LId r J<d z J<4dKC=LIb sr d sz c 2 3
/PE4Ge
&+%'5"#-\8$(),.
$*-!> 2.12 Se(a)d(b)d1M`?!]Q
r J<d z J<"#-\8!Se(c)d(d) d r J<KC=LI4a
AM @X!"#-\8!Se&+%'5"#- r J<
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18
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$ Ag2Br #
241%+
8
5AM "0*6
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19
U9KB5B> 160.93 kHzWS8.U maVAC V1.5 VV
7 2.12 F;BS8 AM 9K"
)+#
(!$0 107 Ag 2 79 Br + O3%&*,'+X
7 2.13 F;BS85B> AM 9K/<+#(
!$:=1+LQSJ@H6XUUV9KB5B> 77.54
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UbV9KB5B> 160.93 kHzWS8.U maVAC V
1.5 V)
RNDF;BS8-CS8PE?AW AM 9KD
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20
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[10] "$903(86540( / FM 1
:- 2 &;
*:1979;
[11] !., / %')+ CQ &*:1983;
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50