P♦s✐tr♦♥ ❆▼❙✲✵✷ ❆♥♦♠❛❧②✿ ❙✐♥❣❧❡ ❙◆❘ ❊①♣❧❛♥❛t✐♦♥ ✇✐t❤♦✉t ❉▼ ♦r P✉❧s❛r ❈♦♥tr✐❜✉t✐♦♥s ▼✐❦❤❛✐❧ ▼❛❧❦♦✈ P❛tr✐❝❦ ❉✐❛♠♦♥❞ ❯❈❙❉ ❘♦❛❧❞ ❙❛❣❞❡❡✈ ❯▼❉ ❙✉♣♣♦rt❡❞ ❜② ◆❆❙❆ ❆str♦♣❤②s✐❝s ❚❤❡♦r② Pr♦❣r❛♠ ✶ ✴ ✶✹
❖✉t❧✐♥❡ ✶ Pr❡❧✐♠✐♥❛r② ■♥❢♦r♠❛t✐♦♥ ❉❙❆ ✲ ❚❤❡ ❉✐✛✉s✐✈❡ ❙❤♦❝❦ ❆❝❝❡❧❡r❛t✐♦♥ ❉❙❆❅❙◆❘✿ ❚❡st P❛rt✐❝❧❡ ✈s ◆♦♥❧✐♥❡❛r ✷ ❉✐s❛❣r❡❡♠❡♥ts ✇✐t❤ t❤❡ st❛♥❞❛r❞ ❉❙❆ ❆♥♦♠❛❧✐❡s ✐♥ ♣♦s✐tr♦♥ s♣❡❝tr✉♠ ❊❳■❙❚■◆● ❡①♣❧❛♥❛t✐♦♥s ❛♥❞ t❤❡✐r ✇❡❛❦♥❡ss❡s ✸ ◆❊❲✿ ▼✐♥✐♠✉♠ ❛ss✉♠♣t✐♦♥s✱ s✐♥❣❧❡ s♦✉r❝❡ ✭❙◆❘✮ s❝❡♥❛r✐♦ e ± ❛s②♠♠❡tr② ♦❢ ❛❝❝❡❧❡r❛t✐♦♥✿ ▼♦❧❡❝✉❧❛r ❈❧✉♠♣s ▼✐♥✐♠✉♠ ✐♥ e + / ( e + + e − ) : ◆▲ ❉❙❆ ✹ ❈♦♥❝❧✉s✐♦♥s✿ ♥♦ r♦♦♠ ✭❛❧♠♦st✮ ❢♦r ❉▼✴P✉❧s❛rs ❝♦♥tr✐❜✉t✐♦♥ ✷ ✴ ✶✹
❊ss❡♥t✐❛❧ ❉❙❆ ✭❛❦❛ ❋❡r♠✐✲■ ♣r♦❝❡ss✱ ❊✳ ❋❡r♠✐✱ ⑦✶✾✺✵s✮ Linear (TP) phase of accelera � on NL, with CR back-reac � on Down- Upstream Down- stream Upstream stream U(x) U(x) x x Sub-shock shock Sca � ering Centers, frozen Into fl ow NL-modi fi ed fl ow ■♥❞❡① q ❜❡❝♦♠❡s q ( p ) ✿ ❈❘ tr❛♣♣❡❞ ❜❡t✇❡❡♥ s♦❢t ❛t ❧♦✇ p ✿ ❝♦♥✈❡r❣✐♥❣ ♠✐rr♦rs✿ q = ✸ r s / ( r s − ✶ ) ∼ ✺ p ∆ x ≈ const ❤❛r❞ ❛t ❤✐❣❤ p : q → ✸ . ✺ ❈❘ s♣❡❝tr✉♠ ❞❡♣❡♥❞s ♦♥ ❢♦r M > ✶✵ , E max � ✶ ❚❡❱ s❤♦❝❦ ❝♦♠♣r❡ss✐♦♥✱ r ✿ ❛❝❝❡❧❡r❛t✐♦♥ ♠✉st ❣♦ f ∼ p − q , q = ✸ r / ( r − ✶ ) ✱ ♥♦♥❧✐♥❡❛r r = q = ✹ ✱ ▼❛❝❤ M → ∞ ✸ ✴ ✶✹
P♦s✐tr♦♥ ❆♥♦♠❛❧② ✭❡①❝❡ss✮ ❚❤✐♥❣s t♦ ♥♦t❡✿ ❘❡♠❛r❦❛❜❧❡ ♠✐♥ ❛t ≈ ✽ ●❡❱ P♦s✐tr♦♥ ❡①❝❡ss ✭❆❝❝❛r❞♦ ❡t ❛❧ ❯♥♣r❡❝❡❞❡♥t❡❞ ❛❝❝✉r❛❝② ✐♥ t❤❡ ✷✵✶✹✮ r❛♥❣❡ ✶✲✶✵✵ ●❡❱ ❖❜s❡r✈❡❞ ❜② ❞✐✛❡r❡♥t ✐♥str✉♠❡♥ts ❙❛t✉r❛t✐♦♥ ✭s❧✐❣❤t ❞❡❝❧✐♥❡❄✮ ❢♦r s❡✈❡r❛❧ ②❡❛rs tr❡♥❞ ❜❡②♦♥❞ ✷✵✵ ●❡❱ ❉r❛♠❛t✐❝❛❧❧② ✐♠♣r♦✈❡❞ st❛t✐st✐❝s ❊❛❣❡r❧② ❛✇❛✐t✐♥❣ ♥❡①t ❞❛t❛ ❜② ❆▼❙✲✵✷ ✭♣✉❜❧✐s❤❡❞ ✐♥ ✷✵✶✹✮ r❡❧❡❛s❡✦ ✹ ✴ ✶✹
❙✉❣❣❡st❡❞ ❡①♣❧❛♥❛t✐♦♥s ♦❢ ♣♦s✐tr♦♥ ❡①❝❡ss ❢♦❝✉s ♦♥ t❤❡ r✐s✐♥❣ ❜r❛♥❝❤ ♦❢ e + / ( e + + e − ) ✐♥✈♦❦❡ s❡❝♦♥❞❛r② e + ❢r♦♠ ❈❘ pp ✇✐t❤ t❤❡r♠❛❧ ❣❛s Pr♦❜❧❡♠s✿ ❚❡♥s✐♦♥s ✇✐t❤ ¯ p ✿ s❡❝♦♥❞❛r✐❡s ✇✐t❤ ❞✐✛❡r✐♥❣ s♣❡❝tr❛ P♦♦r ✜ts✱ ❢r❡❡ ♣❛r❛♠❡t❡rs✱ ♥♦ ♣❤②s✐❝s ♦❢ ✽ ●❡❱ ✉♣t✉r♥✳✳✳ ❆❧t❡r♥❛t✐✈❡ s✉❣❣❡st✐♦♥s✿ P✉❧s❛rs ✭❧❛❝❦✐♥❣ ❛❝❝✉r❛t❡ ❛❝❝❡❧❡r❛t✐♦♥ ♠♦❞❡❧s✮ ❉❛r❦ ♠❛tt❡r ❝♦♥tr✐❜✉t✐♦♥ ❄❄ ❙t❛t✐♥❣ t❤❡ ❖❜✈✐♦✉s ✳✳✳✳ ❉❙❆❅❙◆❘✬ ♣r❡❞✐❝t✐✈❡ ❝❛♣❛❜✐❧✐t② ≫ P✉❧s❛r ♦r ❉▼ ♠♦❞❡❧s → ❉▼✴P✕ ♦♥❧② ✐❢ t❤❡ ❉❙❆❅❙◆❘ ❢❛✐❧s ❯♣s❤♦t ❙◆❘ ❝♦♥tr✐❜✉t✐♦♥ ❝♦♥str❛✐♥s ❉▼✴P✉❧s❛r ❝♦♥tr✐❜✉t✐♦♥s ✺ ✴ ✶✹
❚❤❡ ❲✐s❤❧✐st ❛❝❝♦✉♥t ❢♦r e + ❢r❛❝t✐♦♥ ❜② ❛ s✐♥❣❧❡✲s♦✉r❝❡✱ ❛ ♥❡❛r❜② ❙◆❘ ❡①♣❧❛✐♥ ♣❤②s✐❝s ♦❢ ❞❡❝r❡❛s✐♥❣ ❛♥❞ ✐♥❝r❡❛s✐♥❣ ❜r❛♥❝❤❡s✱ ✽ ●❡❱ ♠✐♥ → ❧❡♥❞s ❝r❡❞❡♥❝❡ t♦ ❤✐❣❤ ❡♥❡r❣② ♣r❡❞✐❝t✐♦♥s ✉♥❞❡rst❛♥❞ ¯ p ✢❛t s♣❡❝tr✉♠ ❛s ✐♥tr✐♥s✐❝✱ ♥♦t ❝♦✐♥❝✐❞❡♥t❛❧✿ ♠♦st ❧✐❦❡❧② ¯ p ❛❝❝❡❧❡r❛t❡❞ s✐♠✐❧❛r❧② t♦ ♣r♦t♦♥s✱ ✇❤❡♥❡✈❡r ✐♥❥❡❝t❡❞ ❇❯❚✿ p / p � = e + / e − ✲ ❲❤② s♦❄ ¯ ♣❧❛✉s✐❜❧❡ ❛♥s✇❡r✿ ❛❝❝❡❧❡r❛t✐♦♥✴✐♥❥❡❝t✐♦♥ ✐s ❝❤❛r❣❡✲s✐❣♥ ❛♥❞ ♠❛ss✴❝❤❛r❣❡ r❛t✐♦ ❞❡♣❡♥❞❡♥t ✉♥❞❡rst❛♥❞ t❤❡ ♣❤②s✐❝s ♦❢ ❝❤❛r❣❡✲s✐❣♥ s❡❧❡❝t✐✈✐t② ✻ ✴ ✶✹
❚❤❡ ❍✐♥ts ✭❑♦✉♥✐♥❡ ❍▲ t❛❧❦ ♦♥ ❙❛t✮ p ❢r❛❝t✐♦♥ ✐s ✢❛t ♦♥ t❤❡ r✐s✐♥❣ e + ¯ ❢r❛❝t✐♦♥ ❜r❛♥❝❤ E > ✽ ●❡❱ ❖♣♣♦s✐t❡ tr❡♥❞s ✐♥ e + / e − ❛♥❞ ¯ p / p s♣❡❝tr❛ ❛t E < ✽ ●❡❱ ❇♦t❤ ❛r❡ ❢r❛❝t✐♦♥s ✱ t❤✉s ❡❧✐♠✐♥❛t✐♥❣ ❝❤❛r❣❡✲s✐❣♥ ✐♥❞❡♣❡♥❞❡♥t ❛s♣❡❝ts ♦❢ ♣r♦♣❛❣❛t✐♦♥ ❛♥❞ ❛❝❝❡❧❡r❛t✐♦♥ ✭st✐❧❧✱ ❍❙ ❡✛❡❝ts❄✮ ❙tr✐❦✐♥❣ s✐♠✐❧❛r✐t② ✇✐t❤ ◆▲ ❉❙❆ s♦❧✉t✐♦♥✱ ❛ss✉♠✐♥❣ ♠♦st ♦❢ e − ❛r❡ ❛❝❝❡❧❡r❛t❡❞ t♦ p − ✹ ✭st❛♥❞❛r❞ ❉❙❆✮ ✼ ✴ ✶✹
❚❤❡ ❆ss✉♠♣t✐♦♥s ❙◆❘ s❤♦❝❦ ♣r♦♣❛❣❛t❡s ✐♥ ✏❝❧✉♠♣②✑ ♠♦❧❡❝✉❧❛r ❣❛s ✭ n ❍ � ✸✵ ❝♠ − ✸ ✱ ✜❧❧✐♥❣ ❢❛❝t♦r f V ∼ ✵ . ✵✶ ✮ ❍✐❣❤✲❡♥❡r❣② ♣r♦t♦♥s ❛r❡ ❛❧r❡❛❞② ❛❝❝❡❧❡r❛t❡❞ t♦ ✭❛t ❧❡❛st✮ E ∼ ✶✵ ✶✷ eV t♦ ♠❛❦❡ ❛ str♦♥❣ ✐♠♣❛❝t ♦♥ t❤❡ s❤♦❝❦ str✉❝t✉r❡ ✭❈❘ ❜❛❝❦ r❡❛❝t✐♦♥✱ ◆▲ s❤♦❝❦ ♠♦❞✐✜❝❛t✐♦♥✮ ❆❝❝❡❧❡r❛t✐♦♥ ♣r♦❝❡ss t❤✉s tr❛♥s✐t✐♦♥❡❞ ✐♥t♦ ❛♥ ❡✣❝✐❡♥t r❡❣✐♠❡ ✭✐♥ ❢❛❝t✱ r❡q✉✐r❡❞ t♦✱ ♦♥❝❡ E � ✶ ❚❡❱✱ M � ✶✵ − ✶✺ ❛♥❞ t❤❡ ❢r❛❝t✐♦♥ ♦❢ ❛❝❝❡❧❡r❛t❡❞ ♣r♦t♦♥s ∼ ✶✵ − ✹ − ✶✵ − ✸ ✮ ❚❤❡ ❙◆❘ ✐s ♥♦t t♦♦ ❢❛r ❛✇❛②✱ ♣♦ss✐❜❧② ♠❛❣♥❡t✐❝❛❧❧② ❝♦♥♥❡❝t❡❞✱ t❤✉s ♠❛❦✐♥❣ s✐❣♥✐✜❝❛♥t ❝♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ ❧♦❝❛❧ ❈❘ s♣❡❝tr✉♠ ❖t❤❡r ❙◆❘s ♦❢ t❤✐s ❦✐♥❞ ♠❛② ♦r ♠❛② ♥♦t ❝♦♥tr✐❜✉t❡ ✽ ✴ ✶✹
■♥t❡r❛❝t✐♦♥ ♦❢ s❤♦❝❦✲❛❝❝✬❞ ❈❘s ✇✐t❤ ❣❛s ❝❧✉♠♣s ✭▼❈✮ ❲✐t❤ s♦♠❡ ❤❡❧♣ ❢r♦♠ ♣❧❛s♠❛ t❡①t❜♦♦❦s✳✳✳ ▼❛①✐♠✉♠ ❡❧❡❝tr✐❝ ✜❡❧❞ ❞✉❡ t♦ e − i ❝♦❧❧✐s✐♦♥s n ✵ E ♠❛① ≃ m e CR e u sh ν ei n i ♠❛①✐♠✉♠ ❊❙ ♣♦t❡♥t✐❛❧ ✐♥s✐❞❡ � ✸ / ✷ � ✶ eV e φ ♠❛① a u sh n CR m p c ✷ ∼ ✶ cm − ✸ ✶ pc c T e ❙❤♦❝❦✲❛❝❝✬❞ ❈❘s ❢♦r♠ ❛ ♣r❡❝✉rs♦r ✿ κ ✲ ❈❘ ❞✐✛✳ ❝♦❡✛✳✱ L p ∼ κ/ u sh ✾ ✴ ✶✹
❊ ✐♥ ▼❈✿ ■♥❥❡❝t✐♦♥✴❛❝❝❡❧❡r❛t✐♦♥ ♦❢ e + ❛♥❞ ¯ p ✐♥t♦ ❉❙❆ ❡❧❡❝tr✐❝ ✜❡❧❞ tr❛♣s e − ❛♥❞ e + ❛r❡ ♦r❡✲❛❝❝❡❧❡r❛t❡❞ ✐♥ ❊ t♦ s♦♠❡ ¯ p ✐♥s✐❞❡ ▼❈ � ✶ ●❡❱ ❛♥❞ r❡❛❞✐❧② ✐♥❥❡❝t❡❞ ❡❥❡❝ts s❡❝♦♥❞❛r② e + ✐♥t♦ ❉❙❆ ❛t E e � ❢❡✇ ●❡❱✱ e + s♣❡❝tr✉♠ → ❝❤❛r❣❡✲s✐❣♥ ❛s②♠♠❡tr② ✐s ❞♦♠✐♥❛t❡❞ ❜② t❤❡ s✉❜s❤♦❝❦ ❝♦♠♣r❡ss✐♦♥ r❛t✐♦✱ r s s♣❡❝tr❛❧ ✐♥❞❡① q = q s ≡ ✸ r s / ( r s − ✶ ) ❛♥❞ t❤❡ s♣❡❝tr✉♠ f e + ∝ p − q s ✳ ❛t ❤✐❣❤❡r ❡♥❡r❣✐❡s✱ ♣❛rt✐❝❧❡s ♣❡r❝❡✐✈❡ ❤✐❣❤❡r ✢♦✇ ❝♦♠♣r❡ss✐♦♥ P▲✲✐♥❞❡① ✐♥s✐❞❡ t❤❡ s♦✉r❝❡ q → ✸ . ✺ ✶✵ ✴ ✶✹
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