) .ƼǂǍɊƳ.>AmJ].')ɕ5

計測の基礎

A

ĉƆmJ].ɱ)0ƀ\R/ɂȶǆƠ/ʄ.Ȼɕ5?B)A

1. はじめにźĻ.

ʖ'/q|ȴƲ/Ė«.')ɕ5A ʕ'Ǐ/«0ȴƲ +Ȳș0 ú¼ǶȀ JISʑJapanesesLĈŢmJ]ɴÞ.<ɪȫ-e*Industrial StandardsʑűƀǄƐȭƋʒʒ=úɸǶ

A+EǙ«*A ʖ'Ǐ<ŵɰʆĀ+ISO ʑ InternationalȀ

Organization

forStandardization ʑ ú ɸ Ɠ ƴ Õ Ɩ Ƒ ʒʒ IEC
ʑInternational Electrotechnical CommissionʑúɸɽơƓƴɆʒʒ*Ɨ/>.ĕȃB)A

îƦũʆĀ/ʖ'/ȯƷ/żǅŅEǙ</*A

2. ビーム計測における性能指数[1]ʚ

q|ȴƲ/ǏǍ0ȴƲʑinstrumentationʒʚ ƽĕ/ǏǍ Eř&)ƼEɬǍ.+?A

EȄǡ



ĖŰ



/ǏǍEɣōA

+

#;/

ůƥŒƛ

!/ǸƈEǅ)őž

ȜǠÏɛâÁ/#;/ŇĂEš¬
0q|/ǟ

ũ³8#0ǦçEǅ)Ȣ/ƼǂɢǞEǂȱA#;/gaEš¬A+*A/āƀǍ-</+)0q|ĶĲɽƩ
|¤Ȃ

+

A

/>.

A

»¦Ǎ.ƲĕĜɇ+-AƼǂɬ0 ÏɛòȏƲĕʑmeasurementʒʚAɬEāƴ+)ǅ
Aɬ+Ɵɑ

q|/ēĕʎ°ʉ-ȴƲ +Ȳș/ůİƨÓ

q|\

?.

q

q|tsGJ-,

uahśÓũZRhśÓũ ÏɛʎîƦ+q|+/¤ǑĨ-,ʆĀENo)A *0İƲĕĜɇǮq|ÈľɀŪ/#;.łȫ-</<A

÷/ȴƲ/%q|.ɱAɄɬEŔ q

ȵ/!B"B.')/ȻɆɃ0ƀ\R|ȴƲ/Ĝɇ+)0

*/èɃEßƹ/+ ,/q|ȴƲ.ɱ

Ũĝ·ȝ·

ŨĝǽɽǗă-,Ȅ?BA *0?.Ǯ÷

)<Eǹ&) ȵ/Ƽǂɬɽơ°ç.ĈŢB)(1) ƲĕĜɇEųǖ.)ǂȱA+ÀǂBA+Ċ+Eńʇ.Ȃ) ɽơ

(2) Ĝɇ.ɤé#ƲĕůƥEɦŗʑȄƍʒ°ç/ȴƲ.ɱAāǘǍ-ƉEɕ5)

A+»¦«+) Fast Current Transformer Eª&)ȴƲ/ƩBJ}[*A>.ȿųEA(3) ȵ/>-ŅȊŚũEųǖ.)ȷȴȨ©ȴƲEȞ+ʚSpan, dynamic range^{jŵ.0ŵɰ/ÈǳȚȅ/ɳǇ*ɕ

5?B-&#Ɖ.')<ɖȵ ȵɕ/ʅSensitivity

ı<ȒĭĈŸ#Resolution8ȴƲZ\f|/Ƒǯ.#&)-ŅȊłȫ.-AȏɃEɕ5A,/>

UncertaintyƗ.

Linearity»¦«+)ɽƩ/ȴƲ.')ȵ/Śũ.

Frequency bandwidth / response timeɱ)ɕ5) ȴƲ/āǘ.0 ɽû ɽƩɪȫ*A[1]ŘŖ-,/ƼǂȴƲ/úɸāƴÙ¤@!

*0ǖɪȫ.-&)A Ėɸ/ăʁ

3. FCT における計測の流れ*<ǖEĎ§.ư?ȴƲ/6+Fȵ/t^\E»¦Ǎ.ȬA#;/«+,EÛ;A+&)<ɢȲ*0- 8úɸā

)

ƴÙ¤

ǖ.ɱAźɓ/ÓëE8+;

ʑFCTʒ.')ȄěA ƲĕĜɇʑÊǭ/ʄǏA Ɨ.ǖ/ċɨÂEōmJ].'(1)ʒ0 /ăéq|ɽƩ*A LlQ

２－ 1

J-PARC MR /"fast current transformer"

ɛĲ/!C&#ȕɽǰđ/ɹõÙ¤ŵɰ¼.
ƽĕ/ŭʁʑFCT ÷:ʁʒEɚɢAɽȕɬ*
J-PARC MR /¸ĝLlQ3 GeV .

A

)0

ȵ/ȕɽǰđ/ɹõ=ocʕ±#@. 41013 ±ʑȷȴ³ʒ/ɵđì8B))185kHz * MR Eîó)A/*îóɽƩ

1 oc/

I1 = [Ǵɽȕ e] ×[ǰđũ] ×[îóîƦũ]=1.6×10ÂĪ/ăé0

3 GeV

𝜏𝜏H

200

𝐼𝐼?XA
𝐼𝐼@A?\

32
64

r  R ³ 0 sinM

2 ²/ 𝐼𝐼@A?\ = 2𝑒𝑒𝑒𝑒G /𝜏𝜏H +-A
30 GeV

unit

80

ns

80
160

A
A

Ũĝ·EŨÁ)Ũĝưȣ+ŨĝÐɊɭ@é0'()

𝐼𝐼?XA = 𝑒𝑒𝑒𝑒G /𝜏𝜏H E Ľ Aĕīƾŋ.-&#q|/ăéʑɽđɵɽđ

(+×4×10 ×185000= 1.18 𝐴𝐴+-A MR *0 8 ocEÏɛA/*q|=ʎLlQɵđáɵđq|ʒ0Gauss ÂĪ*Ȣ+Ċ
8oFaraday cup +ȤȂ>ªDBA B

I8 = 9.47 𝐴𝐴*Ac/îóɽƩq|ɽƩʑɽȕʒ/Ʋĕůƥ+)00q|EƘ;)ɽȕEƲĕA#;~ka+ï1BAʑFig. 2ʒ[2]

Ǖćÿ

q|ɽȕ

>2q|Ƞǣ)ǋǃAʖƗɽđEì
;)¹ɽȕE cup *ɹ;)Ʃ/ɽƩȴ*Ʋĕ-B1-?-/* Cup *Ƙ;A+*-ʎLlQ*0öɼ.-A
/ȯƲłȫ-ăé-,/

?.

ʀǕćÿ

ɡɏ

~ka

łȫ-ăé0ª-Fig. 1 oc/ɽȕÂĪ+ĝĸůoc/¼ɨƑɜEȄA+

ŵ

É+ɽȕĚĲĈÕ)+ňBA
Fig.1 (a).«EǙs ɐ4/ĝĸEȄA+

Fig.1 (b)/>.-A ɽȕĚĲE𝜌𝜌(𝑥𝑥, 𝑦𝑦, 𝑠𝑠), ɽȕ

Fig. 2 Faraday cup /ÝǂøÂĪʑocʒ/ɛĲE𝑣𝑣+A+ ɽƩĚĲ0𝑣𝑣 ∙𝜌𝜌(𝑥𝑥, 𝑦𝑦, 𝑠𝑠)+Ȣ+*A[ref-Jackson]ɽƩĚĲEocŭʁ*ǠÂ#</ɽƩ*𝐼𝐼 (𝑠𝑠 − 𝑣𝑣𝑣𝑣) = 𝑣𝑣

+Ȣ?@ABCDBA

𝜌𝜌(𝑥𝑥, 𝑦𝑦, 𝑠𝑠 − 𝑣𝑣𝑣𝑣)𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

A ɵđq|/ăé.>ªDBAÂĪ
𝑒𝑒𝑒𝑒G
𝑠𝑠 − 𝑣𝑣𝑣𝑣(3 − 1)𝜌𝜌 𝑠𝑠 − 𝑣𝑣𝑣𝑣 = 𝑠𝑠 sinM 𝜋𝜋H
𝑠𝑠H2ʑ0 < 𝑠𝑠 < 𝑠𝑠H ; 𝑒𝑒𝑒𝑒G =𝜌𝜌(𝑠𝑠′)𝑑𝑑𝑑𝑑′ʒEª
𝐼𝐼 (𝑠𝑠 − 𝑣𝑣𝑣𝑣) = 𝑣𝑣

AST

UV /M

sinM (𝜋𝜋

U'XC
UV

)

+-A * 𝑁𝑁G 0oc#@/ǰđũ*

A B08# q|ɽȕ𝑒𝑒𝑒𝑒G = 6.4 𝜇𝜇𝜇𝜇𝜏𝜏H =𝑠𝑠H /𝑣𝑣 / ŵ ɰ ¼ . ɚ ɢ  A  +  ?

ĮýɽƩ

２－ 2

Fig. 3 Current transformer /¼ɨƑɜȂB)A FCTʑfast current transformerʒ[4]E
ʊƂ.+&)

ĳEª&)

ŚũEɆɃAÊǭ*ɕ5#ŅȊ/~ka0Ʃ/½ķÏ

ɛò 3 GeV RCSʑrapid-cycling synchrotronʒ? MR .¸ĝB#q|/ǰđũEī.ȴũ
 ʕŵɰǠǬ³/ɳEɋ->.A#;/ɪȫ-Z\f|/#;/ƏÁò*A

CRǠÂòEǅ#HjSÀǂóɌ.>@ʕ¸ĝFig. 4 Current transformer /óɌƑō[3]ʑɡɏƾƤ.>@ 1 8#0ʖocʒƞ.ǠÂE
ȞHjSɽȕɬ.ĈŢ#</Eg[a!* Current transformerʑh\ʛĈƩòʛɽƩĈōòʒEǅA+Ċ

ÝǂE

.Ǚ
q|ɽƩʑ𝐼𝐼H ʒ>2ƏÁĩǽ/ɽƩʑ𝐼𝐼ʒhJbƾ/ǗŅ¦VH¼.Ǘă
𝜇𝜇B 𝜇𝜇G (𝐼𝐼H + 𝑁𝑁` 𝐼𝐼G )𝐵𝐵 𝑟𝑟, 𝑠𝑠 − 𝑣𝑣𝑣𝑣 =2𝜋𝜋𝜋𝜋EǋǃA Fig.4 *Ǚ#ƏÁVJ.ǐÄ.ŝ
Ǽ#ŘŖ.ǋǃAɽû0 ƏÁVJ/ɮǗƄ/ŵɰĿÂ.ǩ
cd𝑑𝑑
𝜇𝜇B 𝜇𝜇G 𝐼𝐼H + 𝑁𝑁` 𝐼𝐼
𝑉𝑉 = 𝑁𝑁`
𝑑𝑑𝑑𝑑 ∙ 𝑔𝑔
2𝜋𝜋𝜋𝜋
𝑑𝑑𝑑𝑑
ce
𝑑𝑑
𝑅𝑅i
=
𝜇𝜇B 𝜇𝜇G 𝑔𝑔 𝑙𝑙𝑙𝑙
𝑁𝑁 𝐼𝐼 + 𝑁𝑁` 𝐼𝐼
𝑑𝑑𝑑𝑑
𝑅𝑅j ` H
8# /ɽû0ŘŖ*/ɽûɲ.ǩ?
𝑉𝑉 = −𝐼𝐼𝐼𝐼

B??
𝑉𝑉(𝑡𝑡) = 𝑅𝑅EĽAC

𝑑𝑑𝑑𝑑H (𝑡𝑡′) ecCl/m
𝑑𝑑𝑑𝑑′ e'cC/m
𝑁𝑁
𝑑𝑑𝑑𝑑′
`
G

*

Õ)ʕŵɰÂEǠǬ)A
3.1. Dynamic range ʑ Ó © Ǯ ÷ ʒ  > 2
SensitivityʑŊĲʒ

J-PARC MR /źċq|ĶĲ/ȷȴ³0oc#@4×10(+ ±*A źċȜǠocũ

0ʙ±*AB+¸ĝLlQâ@Á

LlQ*/p}a25 ΩEª+𝑁𝑁` = 25 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡h\/p}a0¸ÍɽƩctÁÍɽû~ V
Su

0.64
0.64

160
160

+-A ɳ0 ¸ÍɽƩ/źğ³ 64 A / 1%+
# ȵ.ĊĠ/z[EȄŌ) dynamic
range Eƣ;A+Ȉȫ*A¸Í/ĈÕ.ĜAÁÍ/ĈÕ/ÌéE
sensitivityʑŊĲʒ+ï3(3 − 2)𝑅𝑅i
𝑁𝑁 M
𝐿𝐿 = 𝜇𝜇B 𝜇𝜇G 𝑔𝑔 𝑙𝑙𝑙𝑙
𝑅𝑅j `Eª&# îƦũʆĀ*0
𝑗𝑗𝑗𝑗
𝑅𝑅 𝐼𝐼H𝜔𝜔m
𝑉𝑉 𝜔𝜔 =
(3 − 3)𝜔𝜔 𝑁𝑁`
1 + 𝑗𝑗𝜔𝜔 m
𝜔𝜔m = 𝑅𝑅/𝐿𝐿+-A /ɆɃ*0 VH/Ǹé®ũ=1 q

350BT FCT /ăé0 CR ǠÂò>2Ht/UJEì;)¹¦*
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 1×10(+ 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝/ 𝑉𝑉źċq|ǰđũʚ 1×10(y 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

źċÁÍɽûʚ 10𝑉𝑉

+ȷĕB)A
3.2. Resolution

ResolutionʑÂȱȊʒ0q|ɽȕɬ/ 1-5%E
ǏŚ

4×10(+ ±/ 1-5 %04×10(( - 2×10(M ±|½ǪǒǢbRh>2hJb/ɐ/*@ŁEɚA+Eĕ# 8#

ñʊ+-A/mJ]ʑɺʂʒ*A

?ǋǃA
*0

ƫɠĘɬ

A
V

𝑅𝑅 =

Ȼǵ-ķƾ

-,/ÑƈEƸȮ#

/³EÂȱȊ/ǏƓ³+A

*

mJ]/

ċǏƓÂȱȊEɋ)8+őŽ/Ʋ

MR .¸ĝBAq|ĶĲE~kĕ*--AaA#;. 3-50BTʑBeamTransport-lineʒ.ȷ

２－ 3

mJ].0

ƼǂǁɇEɊƳ

+A</+ĉƆ/mJ]A ƼǂǁɇEɊȁɔǳ 1.7 MHz *Ƴ+AmJ].')ǧ 5 ǥ*Ȼɕ5A

ĕA+ɽû: 8 kVʒłȫ.-A#;¸Í°ç+ÁÍ°ç0ǽķɱ®

ʑlinearityʒE¯'>.ȷȴA ɘ.ǽķɱ®
?/]ȾĨ+-A

3-50BT FCT /ăé040ms .ʕó 2 oc: 2×4×10(+ ±/ɵđɚɢ
AƊƙĩǽEǅŉ)A/* ?b{°çE¸Í) ÁÍɽû+/ǽÿŅ>2ŊĲ1%¼*A+EƞįƊƙ)Aů MR ¼/q|0ǳ 185kHz *îó)A/*

Fig.1 *Ȭ#>-p\ƾ/oc 1 î* 8 ±ʑ+1 ±/ǢoTeʒȯƲBAq|p486 kWʑ2.51×10(y ɵđ/p\ʒ/ŵ.Ʋĕ# 1 «E Fig.5 .Ǚ

ʕƀ/h



\ʕîÂ/°ç*A ¸ĝ?âÁ8*/¹îó/°çEŠ+Ą@'3B)8/*

Ȭ=>. 40ms .ʕhɰĴ)Š)A)A

𝜇𝜇B 𝜇𝜇G 𝐼𝐼H
2𝜋𝜋𝜋𝜋*@ Ėɸ/rRq|ɽƩ Ip = 160 A, V
H×ĺ r = 200 mm .ǩ­-êǟʑFT-3KMʒ

/VH* Ip = 4 A, r = 5 mm /Ƕé*ƲĕEȞ

Fig. 6 .ƲĕůƥEǙ#

ʕƗµ+ʖ

-&#

Ɨµ/óɌǲEÂ)Ǚ# ʖƗµ/ŘŖ³0
'Ⱥ#/Ǹƈ*A

.Ǚ#/0 12.5 *

Fig. 7 0VH+ĩǽ/¿ǒ

8 0ƲĕǸƈ/ 1 «*A

ķʑVinʒ z_aʚʖƗµ/°çƦķʑVoutʒɿʚhOǅp\*AħøȁɔîƦũ300 kHz æø 1 MHz /Ǹƈ*A ȁɔîƦũEA+ÁÍɽû¥A+D
Aʑƀ«*0 1.6 %ʒ

ǿɐ

\EMs^d/>-ȢǙůƥ0zKftdhʑwaterfall plotʒ+ï1BA

Fig. 6 FCT /Ɗƙ

Fig. 7 FCT /Ɗƙ
Fig. 5 MR ¼/ FCT /°çîóq|/ăé.0 VH¼Eɉ DC q|ɽƩōÂ 350BT />-ʕóɚɢ.Ɵ5)îóũʑǳ 185 kʒ².ąA/*

VH¼ǗƄ

ĚĲ/śAȎĈDA ƙǖ.ǖȼA.0q
|+êǞĲ/b{p\Eɚ)ŃǫEƲ
ĕA+Ž8 -@/ȭƔ/p\ɽƳʑp\Ĭʚũ 100ns

Fig.

ʏʚʕƗµ/°çƦ

\/Ìé*

ƕɐ0ʕî¼/ŵɰ0q|ɽƩ*A #$hhq|.>AVH¼ǗƄ

3.3. Linearityɚī50Ɉȕ.¬ǺA+

Fig. 8 FCT /ƊƙrRɽƩ: 160A

２－ 4ȷȴ/ƛɶ* ocɽȕEőŽ/ǱĲ*âĽ*A>.ĩũɈȕŘŖEɦF*AȺ© Ĕō/ƛɶ*ƏȸAłȫA FCT *0
Fig. 5 />-ƲĕucEǅŉîƦũƽŅʑFig.6ʒ>2\fdtŃǫʑFig.7ʒEƲĕ#

Fig. 9 FCT /Ɗƙ\fdtŃǫ/ưȣŵĕũ 𝜏𝜏 𝜏 575 𝜇𝜇𝜇𝜇 ?¥ĀîƦũ 𝜔𝜔m = 2𝜋𝜋𝜋𝜋𝜋277 𝐻𝐻𝐻𝐻 +ǬÁ*Aq|/îƦũ\vRhEȬA+ ȵ/ƽŅã¸B?BA,Æĕ*A ¸ĝ

3.4. Response time / Frequency bandwidthq|/ƦķʑocĬ 200 nsʒ>2îƦũ\vRhE Fig.14

Fig. 12Fig. 14 ocƦķ>2îƦũ\vRh/ŇEĳ*Ȣ+Fig. 10 FCT /Ɗƙ¡ɣɱũ 𝐻𝐻 𝜔𝜔 E

𝑗𝑗𝑗𝑗
𝑅𝑅
𝜔𝜔m
𝐻𝐻 𝜔𝜔 =
𝑗𝑗𝑗𝑗 𝑁𝑁`1+𝜔𝜔 m
FCT /ÁÍɽû0+Ź)Fig. 11 MR FCT /îƦũƽŅ

Eq. (3-3)0𝑉𝑉 𝜔𝜔 = 𝐻𝐻 𝜔𝜔 𝐼𝐼H (𝜔𝜔𝜔+Ȣ+*Aq|/îƦũ\vRh𝐼𝐼H (𝜔𝜔𝜔ċîƦũ
Ǯ÷*𝐻𝐻 𝜔𝜔

Eq. (3-2)
t RF

Fig. 12 "3-50BT" FCT /îƦũƽŅ

; H 𝑡𝑡 = 𝐼𝐼@ sinM 𝜋𝜋C'()~
CV, 𝑇𝑇} ≤ 𝑡𝑡 𝑡𝑡 𝑡𝑡H + 𝑇𝑇}= 0, 𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒.ĜA FCT ÁÍɽû0ȵ/>.A
𝑉𝑉 𝑡𝑡 =

C'…†
2𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋} }𝑉𝑉G∆𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 ' ‡ − cos
2
𝑡𝑡H
𝑡𝑡H
2𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋} }
+
sin
,
2𝜋𝜋𝜋𝜋
𝑡𝑡H

𝑇𝑇} ≤ 𝑡𝑡 𝑡𝑡 𝑡𝑡H + 𝑇𝑇}

Fig. 13 "3-50BT" FCT /\fdtŃǫ

２－ 5

𝑉𝑉G
=
2

}
çŽ(

*
∆𝑉𝑉(𝑡𝑡) =

}
çŽM

𝑒𝑒 '

C'…Œ 'CVC'…Œ
'‡ − 𝑒𝑒‡,+-A

𝑡𝑡H + 𝑇𝑇} < 𝑡𝑡

𝑡𝑡H = 200 𝑛𝑛𝑛𝑛

8#𝑇𝑇} = (𝑛𝑛 − 1) 𝑡𝑡c| : n ǉǏ/oc/ɯďŵɰ
𝑣𝑣𝑒𝑒𝑒𝑒G𝑄𝑄
𝐼𝐼@ ==𝑠𝑠H /2𝑡𝑡H /2
𝑄𝑄: oc#@/ɽȕɬ
1
𝐿𝐿
𝜏𝜏 =
=
𝜔𝜔 m 𝑅𝑅
2𝜋𝜋 M
𝑅𝑅
𝑉𝑉G =
M 𝑁𝑁 𝐼𝐼@𝑡𝑡`
2𝜋𝜋 M + H𝜏𝜏+# 350BT FCT /ŃǫƦķE Fig. 15 .Ǚ

ʀī.ȐƦķE¾ǁ)A+D

A ßȄ/#;. ¥ĀɥŭîƦũ10+ ².-&
#ăé/ȴǬǸƈE Fig. 16 .ǙȾĨEȬǠ<A#;. 𝑡𝑡H ≪ 𝜏𝜏 /ăéƗ8*â@n=1, 2 E!B"Bȹ­A+ɚɢA/*

C'(ç'M)C~
(C'(ç'M)C~ )'CV‡‡𝑒𝑒 '− 𝑒𝑒 '

n = 1 /ŵ0 ∆𝑉𝑉(𝑡𝑡) = 0+A

𝑡𝑡H − 2 𝑛𝑛 𝑡𝑡c“2 𝜏𝜏350BT FCT /ăé0ó.ʖoc
1+

CV
‡

/ʕ

𝑡𝑡c“ = 598 𝑛𝑛𝑛𝑛
𝜏𝜏 = 575 𝜇𝜇𝜇𝜇+)𝑛𝑛 = 10.999

𝑛𝑛 = 2 0.998+-@ÖÂğ+DA

ĖǅǍ.0



/Z\f|0ǽķǲ+ȄA+* q|ƦķĈD? Ù.ċĈÕA$-?
1

ȵ/ȾĨƟ0ĕ+-@*ǑƜA+äȊ+-AȦƙEȞ+#$Ėɸ/q

|Ʀķ0 RCS */Ïɛƅ.>&)ĈÕA/*

êǞĲ/ȾĨǃA

?.Ėɸ/

HjSǠÂò.A CR ǠÂò/îƦũƽŅ
/ĸʃ<ãA

ɕ/>.

!B?Eì;)b{p\EÜÏ)1%¼.-A>.
ƊƙEȞ-&)A

𝑉𝑉 𝑡𝑡
≈

+

2𝜋𝜋{𝑡𝑡 − 𝑇𝑇} }𝑉𝑉G(𝑛𝑛 − 1) 𝑡𝑡H−+ 1 − cos2𝜏𝜏
𝑡𝑡H

𝑡𝑡H sin

2𝜋𝜋{𝑡𝑡 − 𝑇𝑇} }− 2𝜋𝜋{𝑡𝑡 − 𝑇𝑇} }
𝑡𝑡H
,
2𝜋𝜋𝜋𝜋

Fig. 15 "3-50BT" FCT /ŃǫƦķʑȴǬ³ʒ

𝑇𝑇} ≤ 𝑡𝑡 ≤ 𝑡𝑡H + 𝑇𝑇}

𝑉𝑉G 𝑛𝑛 𝑡𝑡H, 𝑡𝑡H + 𝑇𝑇} < 𝑡𝑡 < 𝑇𝑇}’(
2 𝜏𝜏+ɓ£A /ɓ£*0
𝑅𝑅
𝑉𝑉G ≈
𝐼𝐼
𝑁𝑁` @
*A n ǉǏ/ocʑ𝑇𝑇} ≤ 𝑡𝑡 ≤ 𝑡𝑡H + 𝑇𝑇} ʒ/ɓ≈£ķ/{ }¼/ǧʕʄ0Ê/oc/ĸʃ ǧʖ(>2ʗʄ0¥ĀɥŭîƦũʑ ʒƸăé/Ń
‡Fig. 16 ¥ĀɥŭîƦũ𝟏𝟏𝟏𝟏𝟑𝟑 ²ċăé
3.5. 8+;Ȭ)#>. ƲĕĜɇ.Ń)ɤÃ-Ʋ
ĕůƥ/ɦŗ q|p}a.Ń#ȻǵȷǫƦķ ǧʘʄ0¥ĀɥŭîƦũ/°ç¥ȴ.>&) ǏǍ+AŅȊŚũEĖǁA+A+.>Aĸʃ*A ɽȕEƢ;#ŵ/łȫ*AȾĨEȬǠ<A#;.
𝑡𝑡 ≤ 𝑇𝑇}’( ʒEǠÂ+/ƟEƢ;A+n ocǏ/ɨÂʑ𝑇𝑇} ≤ɥŭ/ĸʃ/Ƹăé/³

Ǩȅ/Ƿʍ*0q|+/0-@ss#</* ŵ+ăé*ĈÕA TDRʑTechnical Design Reportʒ/>-２－ 6

ùĕB#p}aȢ.ā()&8&*ǙȾĨEì;)ȢǁB##+>-«<ȬȆ#³ 0Ėɸ.0Ƣ;?B-ɬ*@ ļ&) Ⱦ

ƲĕƅE

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\*0öɼE¢ äȊ-Ǯ÷*ȷȴƛɶ+Ȳș0ªD.

?ȄŌA+ɪȫ$+Ŋ)A.>&)ȢǁA>.ŞčB)A
į.0

4. 物理量の国際基準と不確かさ

ǒ/³ǖ(uncertainty)
1993

ȴƲ.Aǖ/Ȣǁ/OJi(Guide to the expression of Uncertainty in
Measurement: GUM +ǈ)ÈĕB)

4.1. úɸÙ¤ǲ[5]AȴƲǸƈE¹Ǉºɚ/ȲȽ*AúɸÙ¤
ǲʑSIʒ*ȢǁA+0 āƀ/āƀ*A
ű

ǁü0

ǒ/

¨ȥEř&)İA+0 ɚī/ɳ?B#`!/úɸÙ¤ǲ0<Ǔ@Ľ-+.-A



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GUM 0 ISO/IEC Guide 98-3(JCGM 100) +)Ū¶¾ǾB

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/ World Metrology Dayʑúɸȴɬȵńűʒ>@ǖ.ɱAǅȽ+)0/></AʑJIS Z 8103:2000ʒ
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ɤÃ-ʈĲů

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4.2. ȴƲ/ǖ[7-9]úɸĲɬȡĐð

Fig. 17 ǖ.ɱAȴƲǅȽ(CIPM)>2!/Ôġ*AúɸĲɬȡġ(BIPM)šȲ úɸƓƴÕƖ
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ȾĨ = ȴƲ³  ǒ/³

āƀǍ.0

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ǻȴǍ.ŔDBA A

aJt/ǖ+ !Bĉ/ B aJt.Â?BA+Ȅů+A

!)

ȩũ/Ĉũ

𝑥𝑥( , 𝑥𝑥M , … , 𝑥𝑥} ?ɱũ y = f(𝑥𝑥( , 𝑥𝑥M , … , 𝑥𝑥} ) *?

２－ 7BAȴƲĜɇ y /ǖʑ𝑢𝑢š ʒ0 Ĉũ/ǖʑ𝑢𝑢›œ , ⋯ , 𝑢𝑢›† ʒ?éōǖ

M
M
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝑢𝑢›œ + ⋯ +
𝑢𝑢›†
𝜕𝜕𝑥𝑥(
𝜕𝜕𝑥𝑥}

𝑢𝑢š =

EȴǬ)ȹ­A

5. 雑音の種類と物理的背景ɽơ°ç/Ʋĕ.AmJ]0 ƺɺʂ

Fig. 18 ʖ'/ŘŖ¦+śÓ~i[11]ZdhmJ] 1/f mJ] oRnK_mJ]-,@

.ʅƗɕ5)

Ʋĕñ

ʊ+-AmJ]0ȵĉ. ĉɨ?Ư¸Aƒ-ĉƆmJ]@ B?/ɴÞ<ċĈɪȫ*A B.ɱ)0ɂȶǆƠ/Ʌȃ*Ȼɕ
BA

Fig. 19 ƺɺʂ+ŘŖ, ƱĲ[10]5.1.  ƺɺʂŘŖ¦-,/ɽơ¡Ğ¦/¼ɨ* ƺĮȡ.
Aɽđ-,/ɽȕPH/ţÓ.>@mJ]ǋǃA[10,11]

Fig.19 . [10]*ĂíB)A4𝑅𝑅𝑘𝑘H 𝑇𝑇 ∆𝑓𝑓/ɱ

®EǙgaEşɒA
5.2.  Zdh mJ]

Fig.18 .Ǚ>.ʖ'/ŘŖ¦ RI + RII E

ɽƩ/ɊƳ*Aɽđ-,/ɽȕPH0ƽŅJrb\ ZC=RI=RII /¡ɗǽɌ*ŝǼ

ǰđ*A /ǰđũǻȴǍ.1?'+A .ƺLlQ.>&)îƦũ 𝑓𝑓~𝑓𝑓 +.>&)mJ]ǃA BEZdhmJ]∆𝑓𝑓/ɰ.ǋǃAĕüƦ/śÓ~i/ũ0
2ℓ ∆𝑓𝑓,𝑣𝑣
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2ℓ 𝑘𝑘H 𝑇𝑇 ∆𝑓𝑓,
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𝑣𝑣
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*

)

+<A

𝐸𝐸 M
,
4𝑅𝑅
ļ&)mJ]ɊɽÍ0
𝑃𝑃 = 𝐼𝐼 M 𝑅𝑅 =A+Ľ?BA[12]( 𝚤𝚤 − 𝚤𝚤 )M = 2 𝑒𝑒 𝑖𝑖 ∆𝑓𝑓

5.3.  1/f mJ]¥îƦ*ŦɩǍ.-@

ċ8. 1/f .Ɵ«AmJ]ʑsdNmJ]+<ï1BAʒ0
ô0ƒ

*@

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ĶǗŅ¦.ǗăʑHʒEÜÏ)+𝐸𝐸 M = 4𝑅𝑅𝑘𝑘H 𝑇𝑇 ∆𝑓𝑓+-A ɽûƦķ0Įý³ 0 Ɠƴ´Ĩ 4𝑅𝑅𝑘𝑘H 𝑇𝑇 ∆𝑓𝑓

BA+ï3 ɽȕPHũyH`ÂĪ.ļ+ǗĆɝǼ.Ó)oRnK_mJ]ʑBNʒ+
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２－ 8

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0 0.5Hz *A ʖƗVJ°çƦķ/sLĈŢE Fig.21 .Ǚ

ǳ 400Hz /ōÂ0Ǘ

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F=1 ¼ɨɺʂB1 F>1 +-A n ƛ/ǿǼŝǼB#ąĬò/ăé0
𝐹𝐹M − 1 𝐹𝐹+ − 1𝐹𝐹} − 1++⋯+,
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6. 計測例
*oc~ka°çʑWall Current

Monitor, CT +ʌ£/~kaʒ.ɪǊ)AmJ]EîƦũʆĀ*Ndh#«

Wall

Current Monitor °ç/gocŵ/ȯƲ«Eɕ
Fig. 20 ɊǗÍ+oRnK_mJ]ʑBNʒ

5A
6.1. RCS ¸ĝɓ*/oc/VraŭģŤĸʑcomputed tomography; CTʒoc°ç0ǿůë¤ǑǢɰʑt - p/pʒ/ŵɰɐʑtʒ4/ĝĸ*A ɚī/ CT 0ȯƲȤȂEƲĕĜɇ/î@E 360 Ĳó)gaEâA
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Fig. 22 ǳ 400 Hz /Ƶ?-ÐǗŷǽ/ōÂ
Fig. 23 ɚī/ CT +¤ǑǢɰ/ CT[14]２－ 9Ʋĕ#Ʀķga*0 Fig.24 .Ǚ>.

6.2.  gocŵ/ocƦķmJ].>@°çċťB)A s

MR *0LĈŢEA+ mJ]0 Fig.25 ħø.Ǚɛq|âÁ +>.ǳ 330 kHz /ĉƆmJ]*@ q.

|\vRhʚîóîƦũǳ 614 kHz +!/ʎɀƦ?Âɻ*A!/ɨÂENdh)¹q|Eʕó/îó¼*âÁ
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ɟq|âÁ /ʖǟʌ/âÁEȞ-&ɘ)A ɟq|âÁ*0 ocƑɜ.>sLĈŢ.>@ŵɰʆĀ.ŏ#ǸƈAq|ɽƩ/ƶƮƼǂĖʍ/ƏÁò/Ñǀ

Fig.25 æø*A />.mJ]¥ưÀǂ

EȘ+-,/ņĸʃEà7/*#gaE CT ȱƇ)Ľ#¤ǑǢɰ¼/ÂĪâÁÊ.Ïɛ RF ɽûEÃ&)q|/ÂĪEĮþ.

Fig.26 *AAq|ĶĲą)A+q|ēĕŅ

[16]ǋǃ

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&¥ư

>+)AƶƮ¾ǁ)8
MR .ȷȂB# WCM /°çƦķ/îƦũ\vRh/ŞǝEȬA+ʑFig. 27ʒ !/ƒđȐD@ ǁɇ/ȱƇ.ĹǤ' ƕɐ0îƦ
ũ

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67Ïɛ RF ɽûEÃ&#ŵÉ*

æ/ȑ\T*Ǚ>-ɩȑ*Ķ,EȢ)A 1.5 s ?\vRhpĚĲ
Fig. 24 WCM ƦķʑÀǂÊʒ[15]Ųư@ď;A

1.55 s ɓ?¾2ąÏ

 500 MHz 8*İ&)A *< °ç+mJ]/Ã@Âɪȫ.-&)AǁüɞȞ/fz*A

Fig. 25 WCM ƦķʑÀǂĻʒ[15]Fig. 27 gocɲ/\vRh/Şǝ[17]7. まとめȴƲ.#&)0ȁɔ.-A(1) ƲĕĜɇEųǖ.)ǂȱA+(2) Ĝɇ.ɤé#ƲĕůƥEɦŗʑȄƍʒ
A+Fig. 26 RCS ¸ĝĻ/¤ǑǢɰ¼/ÂĪ[15](3) ȵ/>-ŅȊŚũEųǖ.)ȷȴȨ©ȴƲEȞ+ʚ

２－ 10

[12] ɾǆ·, ƎŜƬ,\ , ȧȗŐ, 1984.

Span, dynamic range
Sensitivity[13] ɓȰȇ°,
1984.

Resolution
Uncertainty
Frequency bandwidth / response time»¦«*Ȭ)#>.

/~ka*ȑʕǟʌ-ƼǂɬEȴƲ*A '/ƼǂɬE§ǟʌ/~ka*ȴƲ<*A
è~ka/ƽŅEǂȱ) ƾƤ.Ń)ªÂA+Ȉȫ*A

8# ŮƾƤ.Ĝ

ŃA#;.0 Ů~ka/ɯǋ.c[16] Ȗțǆ ȃÚ, q|/ãAJrb\+q|/ēĕŅ/ǂɃ , OHO2010[17] ƁĤ Ƨ, Ǜ°.

q|~ka/ǋĢ/ƚå*<Aß Ȅ ū ƿ[1] 0;)/ȴƲĦĒ ŧȳǧʖƻ, ØȓČʔſƃɧʔȔſÒ, ɅɁǚ
[2] Chao, Alexander Wu (ed.) ; Tigner, Maury (ed.),Handbook Of Accelerator Physics And
Engineering, World Scientific, 1999.
[3]  ¯ ſ ƪ Î ,OHO2018ɵđq|~ka

,[4] 3-50 BT / FCT 0/ūƿ/ůƥEɍȪ)@ ȷȴȨ©ȅ<ê*AʚȔĥċ,
500 MeV Beam Transport Line /q|ĶĲ~ka , KEK Internal 93-9, 1993.
[5] https://www.bipm.org/en/measurement-units/[6] https://unit.aist.go.jp/nmij/public/report/SI_9th/pd
f/4_SI_HvH.pdf[7] Ĥʐĵɧ,
2017.

ɽơɽđȴƲ/āǘ , ɽơĒ, ȧȗŐ,[15] S. Mukherjee, "Study of Beam Current Monitors",
report for Summer Internship 2019 in KEKSokendai.

[A+<ɦŗȉ+)A Ïɛò/ǋĢ/ƚå0ĶǗŅ¦/Ƽǂ RhkR[14] M. Yoshimoto et al., "LONGITUDINAL PHASESPACE TOMOGRAPHY AT J-PARC RCS",
Proceedings of IPAC2009, pp. 3358-3360.

Linearityɪȫ*AŃǅL,[8] https://dl.cdn-anritsu.com/anritsucustomersupport/ja-jp/reliability/usefulcontents/publication/forn-311.pdf[9] https://unit.aist.go.jp/qualmanmet/nmijico/JCGM/
no19/SQ1802_SP.pdf[10] John Bertrand Johnson, “Thermal Agitation ofElectricity in Conductors”, Physical Review 32,
pp. 97–109, 1928.
[11] Harry Nyquist, “Thermal Agitation of Electric
Charge in Conductors”, Physical Review. 32, pp.
110–113, 1928.

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