MUDIGANTI Jagadish C., 出原敏孝, 小川勇

(1)

マグネトロンン入射型電子銃の設計における電子軌道解析コード(EGUN)の導入

著者山口裕資, 立松芳典, 斉藤輝雄, 池田亮介,

MUDIGANTI Jagadish C., 出原敏孝, 小川勇

雑誌名遠赤外領域開発研究

巻 12

ページ 51‑55

発行年 2011‑06

URL http://hdl.handle.net/10098/3649

(2)

ࡑࠣࡀ࠻ࡠࡦ౉኿ဳ㔚ሶ㌂ߩ⸳⸘ߦ߅ߌࠆ 㔚ሶ゠㆏⸃ᨆࠦ࡯࠼㧔 EGUN 㧕ߩዉ౉

Introduction of electron trajectory code “EGUN” for optimum design of the magnetron injection gun

ጊญ⵨⾗㧘┙᧻⧐ౖ㧘ᢧ⮮ノ㓶㧘ᳰ↰੫੺㧘

Jagadish C. MUDIGANTI

㧘 ዊᎹാ㧘಴ේᢅቁ

Yuusuke YAMAGUCHI, Yoshinori TATEMATSU, Teruo SAITO, Ryosuke IKEDA, Jagadish C. MUDIGANTI, Isamu OGAWA and Toshitaka IDEHARA

⑔੗ᄢቇ㆙⿒ᄖ㗔ၞ㐿⊒⎇ⓥ࠮ࡦ࠲࡯

Research Center for Development of Far-Infrared Region, University of Fukui Fukui 910-8507, Japan

Abstract

We have introduced a relativistic electron trajectory code EGUN (W.B. Herrmannsfeldt, SLAC-331 (1988), [1]) to design Magnetron Injection Guns (MIG) for new gyrotrons. In EGUN, an axisymmetric Poisson’s equation is solved by the finite difference method for evaluation of the distribution of the electrostatic potential between the electrodes. In addition to the structure of the electrodes, the external magnetic field can be set in the axisymmetric geometry. The electron trajectory in the applied electromagnetic field is calculated with a relativistic equation of motion by using the Runge-Kutta method.

In this study, a comparison of the calculated result is made between EGUN and other code EPOSR [2] for check on validity and applicability of EGUN. Pre- and post-processing codes have been developed for EGUN for efficient design of new MIG’s. We have just started design optimization of a new MIG for an advanced gyrotron (300 GHz, 100 kW).

研究報告５

(3)

1

㧚⎇ⓥ⢛᥊ߣ⋡⊛

㆙⿒ᄖ㗔ၞ㐿⊒⎇ⓥ࠮ࡦ࠲࡯ߢ㐿ᆎߒߚࠫࡖࠗࡠ࠻ࡠࡦߩ㜞ᐲൻ⎇ⓥߦ߅޿ߡߪ㧘ᒝ

⏛႐ㇱߦ⟎߆ࠇߚዊඨᓘ౒ᝄེߦ․ᕈߩ⦟޿㔚ሶࡆ࡯ࡓࠍ౉኿ߔࠆߎߣߩ಴᧪ࠆ㔚ሶ

㌂߇᳞߼ࠄࠇࠆ㧚㆙⿒ᄖ㗔ၞ㐿⊒⎇ⓥ࠮ࡦ࠲࡯ߢߪ㧘ߎࠇ߹ߢ㔚ሶ㌂⸳⸘ߩὑߩኾ↪ࠦ

࡯࠼߇ήߊ㧘ߘߩᢛ஻ߪᕆോߣߥߞߡ޿ࠆ㧚ߘߎߢ㔚ሶ゠㆏⸃ᨆࠦ࡯࠼㧔EGUN [1]㧕 ߇ᣂߚߦዉ౉ߐࠇߚ㧚ᧄ⎇ⓥߢߪ㧘ല₸⊛ߦ㔚ሶ㌂⸳⸘ࠍⴕ߁ὑߩࠪࡒࡘ࡟࡯࡚ࠪࡦⅣ Ⴚߩ᭴▽ࠍ⋡⊛ߣߒߚ㧚

2

㧚㔚ሶ゠㆏⸃ᨆࠦ࡯࠼ ̍

EGUN

̍ ߩዉ౉

2-1 EGUNߩ᭎ⷐ

EGUNߪ㧘SLAC㧔Stanford Linear Accelerator Center㧕ߢ1982ᐕߦ㐿⊒ߐࠇߚ㧘㔚ሶḮ

⸃ᨆߩߚ߼ߩ᳢↪ੑᰴరࠦ࡯࠼ߢ޽ࠆ㧚ߎࠇ߹ߢ㧘ടㅦེ߿⊒ᝄ▤ߥߤߩ㔚ሶḮ⸳⸘ߦ ߅޿ߡ㧘਎⇇⊛ߦ೑↪ታ❣߇޽ࠅା㗬ᕈ߇㜞޿㧚㒶ᭂ߆ࠄߩ㔚ሶ᡼಴⸘▚ߢߪ㧘᷷ᐲ೙

㒢᡼಴㧘Child-Langumuir ೣߦၮߠߊⓨ㑆㔚⩄೙㒢᡼಴㧘෸࡙߮࡯ࠩߦࠃࠆೋᦼ⸳ቯߦ

ၮߠߊ㔚ሶ᡼಴ࠍขࠅᛒ߁ߎߣ߇น⢻ߣߥߞߡ޿ࠆ㧚㔚⏛⇇ਛߩ⩄㔚☸ሶߩ゠㆏⸘▚ߢ ߪ㧘ⓨ㑆㔚⩄ߩᓇ㗀㧘⥄Ꮖ⏛႐ߩᓇ㗀㧘ਗ߮ߦ⋧ኻ⺰⊛ലᨐ߇⠨ᘦߐࠇߡ߅ࠅ㧘ࠫࡖࠗ

ࡠ࠻ࡠࡦߢ૶↪ߐࠇࠆࡑࠣࡀ࠻ࡠࡦ౉኿ဳ㔚ሶ㌂㧔Magnetron Injection Gun : MIG㧕ߩ⸃

ᨆߦ߽ㆡ↪ߔࠆߎߣ߇น⢻ߢ޽ࠆ㧚

㔚ሶ゠㆏⸘▚ߩᵹࠇ࿑ࠍਅߦ␜ߔ㧚࡙࡯ࠩߪ㧘㔚ᭂ㈩૏ߦၮߠߊ⸘▚㗔ၞߩⷐ⚛ಽഀ

ߩᖱႎ㧘⏛႐㈩૏㧘෸߮㔚ሶ᡼಴ߩ᧦ઙࠍਈ߃ࠆ㧚EGUNߢߪ㧘ゲኻ⒓♽ߦ߅ߌࠆࡐࠕ

࠰ࡦᣇ⒟ᑼ߇Ꮕಽᴺߦࠃߞߡ⸃߆ࠇ㧘 ⷐ⚛▵ὐ਄ߩ㕒㔚ࡐ࠹ࡦࠪࡖ࡞㧘ߘߒ ߡ㔚⇇ಽᏓ߇⸘▚ߐࠇࠆ㧚ᰴߦ㧘⋧ኻ

⺰ ല ᨐ ࠍ ฽ ߻ ㆇ േ ᣇ ⒟ ᑼ ߇ Runge-Kuttaᴺߦࠃߞߡ⸘▚ߐࠇ㧘㔚⏛

⇇ਛߩ㔚ሶ゠㆏߇᳞߼ࠄࠇࠆ㧚ⓨ㑆ߩ 㔚⏛⇇ಽᏓߪ㧘㔚ᭂߣᄖㇱ⏛႐ߩ㈩૏

ߦട߃㧘㔚ሶࡆ࡯ࡓ߇૞ࠆⓨ㑆㔚⩄ಽ Ꮣߣ⥄Ꮖ⏛႐ߦ߽ᓇ㗀ࠍฃߌࠆ㧚ߒߚ ߇ߞߡ㧘ⓨ㑆ߩ㔚⏛⇇ਛಽᏓߣ㧘ߘߩ ਛࠍㆇേߔࠆ㔚ሶߩ゠㆏ࠍ⥄Ꮖή᠓⌕

ߦ⹏ଔߔࠆὑߦ㧘➅㄰ߒ⸘▚߇ᔅⷐߣ ߥࠆ㧚ᦨ⚳⊛ߦ㧘㔚ሶ゠㆏߇෼᧤ߒߚ ߣߎࠈߢ➅㄰ߒࠍᱛ߼㧘⸘▚⚿ᨐࠍ಴

㔚ᭂ᭴ㅧ㧘⏛႐㈩૏ߩ⸳ቯ

ⓨ㑆ࡔ࠶ࠪࡘߩ૞ᚑ

㕒㔚ࡐ࠹ࡦࠪࡖ࡞ಽᏓߩ

⸘▚㧔Ꮕಽᴺ 㧕㧘㔚⇇ಽᏓߩ⸘▚

㔚ሶ゠㆏ߩ⸘▚

Runge Kutta ᴺ㧕

゠㆏⸘▚ߩ

෼᧤್ቯ

ⓨ㑆㔚⩄㧘⥄Ꮖ⏛႐ࠍ⠨ᘦߒ 㧘 ᣂߒ޿㔚⏛⇇ಽᏓࠍ⸘▚

⸘▚⚿ᨐ OK

NO

(4)

2-2 EGUN⸘▚ߩ೨ᓟಣℂࠦ࡯࠼ߩ૞ᚑ

EGUNߦኻߔࠆ⸘▚⸳ቯߩ౉ജߪ㧘ᚲቯߩᦠᑼߦၮߠ޿ߡ⸥ㅀߐࠇߚࡈࠔࠗ࡞ࠍ↪޿

ߡⴕ߁㧚EGUN߳ߩ౉ജࡈࠔࠗ࡞ߦߪ㧘ⓨ㑆ࡔ࠶ࠪࡘߩᄢ߈ߐ㧘㔚ᭂᒻ⁁ࠍ⴫ߔᐳᮡ࠺

࡯࠲㧘ฦ㔚ᭂߩ㔚૏㧘㒶ᭂߩ㔚ᵹ᡼಴⸘▚ߩᚻᴺ⸳ቯ㧘㔚ሶ゠㆏⸘▚ߩ㐿ᆎᐳᮡ╬߇฽

߹ࠇࠆ㧚․ߦ㧘MIG ߩ⸳⸘ߢߪ㧘㔚ᭂ᭴ㅧࠍᦨㆡൻߔࠆ૞ᬺ߇ਥߣߥࠆὑ㧘᭽ޘߥᒻ

⁁ߩ㔚ᭂࠍ◲නߥᠲ૞ߢ⸳ቯߢ߈ࠆߎߣ߇㧘⸳⸘ࠍല₸⊛ߦㅴ߼ࠆ਄ߢ㕖Ᏹߦ㊀ⷐߣߥ ࠆ㧚ᧄ⎇ⓥߢߪ㧘㔚ᭂᒻ⁁࠺࡯࠲ࠍEGUN߳ߩ౉ജࡈࠔࠗ࡞ߩᦠᑼߦᓥߞߡ಴ജߔࠆ㧘 ೨ಣℂࠦ࡯࠼ࠍ૞ᚑߒߚ㧚࿑2ߦ㧘೨ಣℂࠦ࡯࠼߇ขࠅᛒ߁ߎߣߩߢ߈ࠆ⸘▚㈩૏ߩ଀

ࠍ␜ߔ㧚࿑ਛߦ␜ߔㇱಽߩ㐳ߐࠍోߡਈ߃ࠆߣ㧘㔚ᭂᒻ⁁ߪ৻ᗧ⊛ߦ᳿߹ࠆ㧚࡙࡯ࠩߪ㧘

࿑ਛߦ␜ߒߚᄌᢙߩ୯ࠍਈ߃ࠆߎߣߢ㧘㔚ᭂ᭴ㅧࠍ⸳ቯߔࠆ㧚ߎߩ೨ಣℂࠦ࡯࠼ࠍ೑↪

ߔࠆߎߣߦࠃࠅ㧘ᓥ᧪ EGUN ߳ߩ౉ജࡈࠔࠗ࡞ߩ૞ᚑߦᔅⷐߛߞߚᾘ㔀ߥᚻ⸘▚߇ਇ ⷐߣߥߞߚ㧚

㔚ሶ゠㆏⸘▚ߩ⚿ᨐߩ଀

ࠍ㧘࿑2-2ߦ␜ߔ㧚࿑ߦߪ㧘㒶ᭂߩ㔚ᵹ᡼಴㕙ࠍ಴⊒ߔ ࠆ㧘9ᧄߩ㔚ሶ゠㆏߇ឬ߆ࠇ ߡ޿ࠆ㧚ฦ㔚ሶߪ㧘㔚ᭂ㑆 ߩ㔚⇇ߦࠃߞߡടㅦߐࠇ㧘

⏛ജ✢ߦᴪߞߡⲷᣓㆇേߔ ࠆ㧚㔚ሶࡆ࡯ࡓߩࠫࡖࠗࡠ

࠻ࡠࡦ߳ߩㆡ↪ߦ߅޿ߡߪ㧘

⏛ജ✢ߦု⋥ߥㅦᐲᚑಽߣ ਗⴕߥᚑಽߩᲧ㧔ࡇ࠶࠴ࡈ

LC

RC 1/2 LC

ZK DC RK

DD

DD CB

LF

LB RB

DE

DB

R

Z 1st ANODE

CATHODE

LF LB

2nd ANODE

DE

(BODY)

RM

DI ZI

INSULATION

θ

B-Field Line

࿑2-1㧚⸘▚㈩૏ߩ଀

0 150 300 450 600 750

0 200 400 600 800 1000 1200

R [Mesh Unit ( = 0.1 mm ) ]

Z [Mesh Unit ( = 0.1 mm ) ]

࿑2-2㧚゠㆏⸘▚⚿ᨐߩ଀

(5)

ࠔࠢ࠲ =

v

A/

v

_//㧕߇㧘㊀ⷐߥ‛ℂ㊂ߣߥࠆ㧚ࡇ࠶࠴ࡈࠔࠢ࠲ߪ㧘౒ᝄེߦ߅޿ߡᄢ߈

޿⒟⦟ߊ㧘߹ߚࡆ࡯ࡓᢿ㕙ౝߢߩಽᢔ߇ዊߐ޿߶ߤ⦟޿ߣߐࠇࠆ㧚ࡇ࠶࠴ࡈࠔࠢ࠲ߩᐔ ဋ୯ߣಽᢔߪ㧘MIG ߩᕈ⢻ࠍ᳿߼ࠆ㊀ⷐߥᜰᮡߢ޽ࠅ㧘Ᏹߦ୯ࠍ⏕⹺ߒߟߟ⸳⸘ࠍㅴ

߼ࠆᔅⷐ߇޽ࠆ㧚EGUNߪMIG⸳⸘ߦ․ൻߒߚࠦ࡯࠼ߢߪήߊ㧘⸘▚⚿ᨐߪ㧘ฦ゠㆏

਄ߩㅦᐲᖱႎ߇⸥㍳ߐࠇߚࡃࠗ࠽࡝ࡈࠔࠗ࡞ߢ಴ജߐࠇࠆ㧚ߎߎߢߪ೨ಣℂࠦ࡯࠼ߦട ߃㧘಴ജࡈࠔࠗ࡞߆ࠄฦ゠㆏ߩㅦᐲᖱႎࠍ᛽಴ߒ㧘ㅦᐲߩᐔဋ୯ߣಽᢔࠍ಴ജߔࠆ㧘ᓟ ಣℂࠦ࡯࠼ߩ㐿⊒߽ⴕߞߚ㧚એਅߦ㧘

v

_Aߦኻߔࠆㅦᐲಽᢔߩ⸘▚ᴺࠍ␜ߔ㧔ࡇ࠶࠴ࡈ ࠔࠢ࠲╬㧘ઁߩ႐ว߽ห᭽ߢ޽ࠆ㧕㧚ฦ゠㆏߇ᜂ߁㔚⩄㊂߇⇣ߥࠆὑ㧘✚๺ࠍ⸘▚ߔࠆ 㓙ߦ㧘ฦ゠㆏਄ߩ୯ߦ㔚⩄㊂ࠍ㊀ߺઃߌߒߡ޿ࠆ㧚ࠫࡖࠗࡠ࠻ࡠࡦ㐿⊒ߦ߅޿ߡ㧘㔚ሶ ࡆ࡯ࡓߩಽᢔߣߒߡ৻⥸⊛ߦᐢߊ೑↪ߐࠇߡ޿ࠆߩߪ࿑2-3ਛߩ̌Delta̍ ߢ޽ࠆὑ㧘 ᧄ⎇ⓥߢ߽ಽᢔߣߒߡ Deltaࠍណ↪ߔࠆ㧚

࿑2-4ߦ㧘ㅦᐲಽᢔߩ⸘▚

⚿ᨐߩ଀ࠍ␜ߔ㧚Z = 50 ~

150 mm ߩ㗔ၞߢߪਥߦ㔚

⇇ߩⓨ㑆ಽᏓߦࠃߞߡ㧘Z >

150 mm ߩ㗔ၞߢߪਥߦ⏛

᳇࿶❗ߩჇᄢߦࠃߞߡ㧘ㅦ ᐲಽᢔߦᄢ߈ߥᄌൻ߇⊒↢

ߒߡ޿ࠆ㧚MIG⸳⸘ߦ߅޿

ߡߪ㧘ᢙ%એਅߩㅦᐲಽᢔ

> @

) z ( v

) z ( v ) z ( ) v

z ( v : Delta

v

) z ( v ) z ( v ) z ( W )

z ( v

: Spread

) z ( W

) z ( v ) z ( W )

z ( v

: Average

) z ( v / I ) z ( W

: Weight

AVG MIN DELTA MAX

AVG

2 1

j

2 j AVG

j SPREAD

j j

j j j

AVG

//j bj j

A A A A

A A A

A

A A

¸¸¹

¨¨ ·

©

§

¦

࿑2-3㧚ࡆ࡯ࡓ਄ߩㅦᐲᐔဋߣಽᢔߩ⸘▚

j㧦゠㆏⇟ภ㧔1㨪゠㆏ߩᢙ㧕

I

b^{㧦ࡆ࡯ࡓ㔚ᵹ}

v

//㧦⏛႐ߦᐔⴕߥㅦᐲᚑಽ

v

A㧦⏛႐ߦု⋥ߥㅦᐲᚑಽ AVG㧦ᐔဋ୯ࠍ⴫ߔ

MAX㧦ᦨᄢ୯ࠍ⴫ߔ MIN㧦ᦨዊ୯ࠍ⴫ߔ

0 0.5 1 1.5 2 2.5

0 100 200 300 400 500 600

Delta Vpara/C Delta Vperp/C Delta Pitch Factor

Z [mm]

Delta-Vpara, Delta-Vperp, Delta-Pitch Factor

(6)

3

㧚ઁߩ㔚ሶ゠㆏⸃ᨆࠦ࡯࠼

”EPOSR”

ߣߩ⸘▚⚿ᨐߩᲧセ

EGUNࠍ೑↪ߒߚ㔚ሶࡆ࡯ࡓ⸃ᨆߩᅷᒰᕈࠍ⺞ߴࠆὑ㧘V.N.Manuilovᢎ᝼߇౒ห⎇ⓥ

ߦ߅޿ߡEPOSRࠦ࡯࠼[2]ࠍ↪޿ߡⴕߞߚࡆ࡯ࡓ⸃ᨆߣ㧘⚿ᨐߩᲧセࠍⴕߞߚ㧚Ყセߦ

ߪ㧘 400 GHzᏪ㧘100 kW⚖ߩ╙ੑᰴ㜞⺞ᵄࡄ࡞ࠬࠫࡖࠗࡠ࠻ࡠࡦ↪ߦⴕࠊࠇߚ㧘MIG ߩ⸳⸘⸘▚[3]ࠍ೑↪ߒߚ㧚࿑3-1ߦ㧘ࡆ࡯ࡓ㔚ᵹߦኻߔࠆࡇ࠶࠴ࡈࠔࠢ࠲ߩᐔဋ୯ߣ

v

_A ߩಽᢔߩᄌൻࠍ␜ߔ㧚EGUNߣEPOSRߩ⸘▚⚿ᨐߪ㧘ห᭽ߩ௑ะࠍ␜ߒ㧘㔚ᭂߩ᭴ㅧ

᳿ቯߦኻߒߡหߓᜰ㊎ࠍਈ߃ࠆߎߣࠍ⏕⹺ߒߚ㧚

4

䋮䉁䈫䉄

ࠫࡖࠗࡠ࠻ࡠࡦߩ㜞ᐲൻ⎇ⓥߦ߅޿ߡ㧘㜞ᕈ⢻㔚ሶ㌂ߩ⸳⸘ᚻᴺࠍ₪ᓧߔࠆὑ㧘㔚ሶ

゠㆏⸃ᨆࠦ࡯࠼㧔EGUN㧕ࠍᣂߒߊዉ౉ߒߚ㧚⸘▚ߩ೨ᓟಣℂࠦ࡯࠼ࠍ㐿⊒ߒ㧘⸳⸘⸘

▚ࠍല₸⊛ߦⴕ߁ὑߩⅣႺᢛ஻ࠍⴕߞߚ㧚߹ߚ㧘೎ࠦ࡯࠼㧔EPOSR㧕ߦࠃࠆ⸘▚⚿ᨐߣ ߩᲧセࠍⴕ޿㧘⸘▚⚿ᨐߩᅷᒰᕈࠍ⏕⹺ߒߚ㧚੹ᓟ㧘ታ⸳⸘߳ㆡ↪ߒ㧘ᣂߒ޿㔚ሶ㌂ߩ 㐿⊒ࠍㅴ߼ࠆ੍ቯߢ޽ࠆ㧚

ෳ⠨ᢥ₂

[1] Herrmannsfeldt W B 1979 Electron Trajectory Program SLAC-226, last version SLAC-331 (1998), Stanford University

[2] Lygin V K, Manuilov V N and Tsimring Sh E 1987 Elektronnaya tekhnika Ser. 1 Elektronika SVCh Vyp. 7 36–38

[3] V.H.Manuilov, FIR FU Seminar, 27/Sep./2010

0.0 0.5 1.0 1.5 2.0 2.5

0.00 0.05 0.10 0.15 0.20

0 2 4 6 8 10

Pitch Factor (EPOSR) Pitch Factor (EGUN) Delta V-perp./C (EPOSR) Delta V-perp./C (EGUN)

Pitch Factor Delta V-perp./C

Beam Current [A]

࿑3-1㧦⸘▚⚿ᨐߩᲧセ

MUDIGANTI Jagadish C., 出原 敏孝, 小川 勇

マグネトロンン入射型電子銃の設計における電子軌 道解析コード(EGUN)の導入

著者 山口 裕資, 立松 芳典, 斉藤 輝雄, 池田 亮介,