Vacuum System in Accelerator

Transcription

1 Vacuum System in Accelerator -- geometrical structure effects on the pumping delay time -- Y. Saito, KEK, Tsukuba, Japan N. Matuda, Tokyo Denki Univ., Tokyo, Japan 1. Required vacuum condition; what kind of vacuum is required? 2. Outgassing of material surfaces and Geometrical structure of vacuum system. 3. Pressure distribution and pumping delay time; MC simulation? Diffusion Eq.?

2 vacuum system: required condition **Clean Vacuum minimizing surface contamination fast pump-down process less impurity in thin film and surface devices **Hot Vacuum minimizing secondary emission; subject to high energy particles electrical breakdown suppression beam instability inhibition; p/e stimulated desorption **Quiet Vacuum minimizing density fluctuation; residual gas molecules reduction of noise in laser interferometer for gravitational wave detection precise measurement in extra high vacuum

3 vacuum system: required condition **Clean Vacuum minimizing surface contamination fast pump-down process less impurity in thin film and surface devices 1 4 nv 1 4 nvs p nkt

4 vacuum system: required condition **Clean Vacuum minimizing surface contamination fast pump-down process less impurity in thin film and surface devices **Hot Vacuum minimizing secondary emission; subject to high energy particles electrical breakdown suppression beam instability inhibition; p/e stimulated desorption **Quiet Vacuum minimizing density fluctuation; residual gas molecules reduction of noise in laser interferometer for gravitational wave detection precise measurement in extra high vacuum

5 vacuum system: required condition **Hot Vacuum minimizing secondary emission; subject to high energy particles electrical breakdown suppression beam instability inhibition; p/e stimulated desorption SEE n(z)g(z)dz B 1 de(z) exp z dz dz escaped from bulk generated in bulk scattered in bulk SEE filmcaoated exp t thickness B film 1 de(z) exp z dz dz

6 vacuum system: required condition **Clean Vacuum minimizing surface contamination fast pump-down process less impurity in thin film and surface devices **Hot Vacuum minimizing secondary emission; subject to high energy particles electrical breakdown suppression beam instability inhibition; p/e stimulated desorption **Quiet Vacuum minimizing density fluctuation; residual gas molecules reduction of noise in laser interferometer for gravitational wave detection precise measurement in extra high vacuum

7 vacuum system: required condition **Quiet Vacuum minimizing density fluctuation; residual gas molecules reduction of noise in laser interferometer for gravitational wave detection precise measurement in extra high vacuum P(x) N C x 1 v V P(x) nv x x! Nx x v V Binomial distribution finding probability of x molecules in small volume v; total molecules of N in volume V e nv, when N and V ( v V n const.) Poisson s distribution P(x) P(x) 2 nv pressure reduction is necessary to reduce fluctuation (deviation)

8 outgassing of material surface and geometrical structure of system **Clean Vacuum minimizing surface contamination **Hot Vacuum minimizing secondary emission; subject to high energy particles **Quiet Vacuum minimizing density fluctuation; residual gas molecules outgassing reduction and surface passivation removal of degraded layer, thin/dense oxidized layer, D hydrogen degassing, 2 p(r, t) H(r) A(r) geometrical structure and pump configuration pressure distribution, control of gas flow, estimation of pumping time and delay time, q(r, t) p(r, t)s(r, t) p(r, t) t p Q S

9 outgassing of material surface and geometrical structure of system Q (x) A p (x) q (x) p (x+dx) s(x) H Q (x+dx) Q ADp(r, t) D 2 p(r, t) H(r) A(r) Q(x) AD 2 p(x,t) x 2 Q(x) Ax p(x,t) t x Diffusion Equation q(r, t) p(r, t)s(r, t) p(r, t) t Hx q(x) in molecular flow region D v (; effective mean free path) *geometrical structure 3 *pump configuration C(conductance) AD (when A is constant) L *outgassing distribution pressure distribution can be calculated

10 outgassing of material surface and geometrical structure of system in molecular flow region *uniform outgassing D 2 p(r, t) H(r) p(r, t) q(r, t) s(r, t) *steady-state A(r) t *circular tube (d: dianeter, L: length) p(x) 2qL2 dd x 2 L 2qL2 dd (p p L ) x L p p 1E _ Beam off 21626_ 63 kw operation p L x= x=l pressure [Pa] 1E-5 1E-6 J-PARC 3 GeV ring 1E distance [m]

11 outgassing of material surface and geometrical structure of system Networked conduit tubes in molecular flow region *uniform outgassing *steady-state *circular tube (d: dianeter, L: length) P i S 11 S n1 Q ij (i) O Q ij C ij S ij O Q ij (j) S 1n S nn P j Q ij (i) (1 )Q ij C ij (p i p j ) Q ij ( j) Q ij C ij ( p i p j ) j Q ij ( j) S i P i continuity condition at every node P 1 Q* 1 M M, S ij (S i, C ij), G * ij ih h P n Q* n G ih

12 outgassing of material surface and geometrical structure of system pressure distribution in KEK 3.5 GeV linac *multi-looped network RF waveguide klystron pump acc. guides S 11 S n1 O S ij O S 1n S nn P 1 Q* 1 M M P n Q* n e - beam p ij (x) 2qL2 dd 2 x 2qL2 L dd (P P ) i j x L P i pumping tube a unit of linac (8 m long)

13 outgassing of material surface and geometrical structure of system pressure distribution in KEK 3.5 GeV linac *multi-looped network klystron pump RF waveguide acc. guides e - beam pumping tube a unit of linac (8 m long)

14 geometrical structure; pumping delay time pressure [Pa] 1E+5 1E+4 1E+3 1E+2 1E+1 1E+ 1E-1 1E-2 pumping down characteristics c/a-1 u/b-1 c.jig-1 s.jig-1 delay When L/d = 5,, averaged hitting times of molecules desorbed from the lamination surface is 1 7. Suppose = 1-4 s, delay is order of 1 3 s or an hour. 1E-3 1E-4 1E-5 1E-4 1E-3 1E-2 1E-1 1E+ 1E+1 1E+2 time [h] Pump down characteristics in compressed and un-compressed laminations. A 1 of stainless steel laminations of 1 mm square,.1 mm thick. They are stacked and compressed. Every gap is roughly estimated as about 2 micrometers: L/d = 5,.

15 geometrical structure; pumping delay time When Xe gas is introduced into the tube of 4-m long and.4 m in diameter, it requires 5 minutes to observe the pressure rise at the end. TAMA 3: interferometer of gravitational wave detector

16 geometrical structure with high aspect ratio; pressure distribution and pumping delay time Pressure Distribution : hitting number of molecules per unit area, per unite time impinging rate 1 4 nv v 4kT p Pumping Delay Time N h : hitting times per molecule, from desorption till escaping T delay N h v surface Histogram Number of molecule sueface ; surface sojourn time /v; flight time in space Monte Carlo Simulation? or Analytical Solution? position in structure x hitting times N h

17 geometrical structure with high aspect ratio; pressure distribution and pumping delay time Pressure Distribution : hitting number of molecules per unit area, per unite time impinging rate 1 4 nv v 4kT p position in structure x Pumping Delay Time N h : hitting times per molecule, from desorption till escaping T delay N h v surface Histogram Number of molecule sueface ; surface sojourn time /v; flight time in space Monte Carlo Simulation? or Analytical Solution? Q ADp(r, t) Diffusion Equation D 2 p(r, t) H(r) p(r, t) q(r, t) p(r, t)s(r, t) A(r) t hitting times N h

18 geometrical structure with high aspect ratio; pressure distribution and pumping delay time Pressure Distribution : hitting number of molecules per unit area, per unite time impinging rate 1 4 nv v 4kT p position in structure x Pumping Delay Time N h : hitting times per molecule, from desorption till escaping T delay N h v surface Histogram Number of molecule sueface ; surface sojourn time /v; flight time in space Monte Carlo Simulation? or Analytical Solution? Q ADp(r, t) Diffusion Equation D 2 p(r, t) H(r) p(r, t) q(r, t) p(r, t)s(r, t) A(r) t hitting times N h

19 geometrical structure with high aspect ratio; pressure distribution (circular disks with a distance d) 1 p(r) 3q 8vd 2 R2 r 2 R d uniform outgassing D 2 p r 2 1 r 1 p(r) p r q d 3Q 4vd 2 steady state lnr ln r localized outgassing normalized pressure,8,6,4,2 R/d = 25 R/d = 25 R/d = E-5 x^2 normalized pressure,8,6,4,2 R/d = 25 R/d = 25 R/d = 25 a-b ln[r] r [position] r [position]

20 geometrical structure with high aspect ratio; pressure distribution and pumping delay time Pressure Distribution : hitting number of molecules per unit area, per unite time 1 4 nv v 4kT p Pumping Delay Time N h : hitting times per molecule, from desorption till escaping T delay N h v surface sueface ; surface sojourn time /v; flight time in space impinging rate position in structure x Histogram Number of molecule hitting times N h

21 geometrical structure with high aspect ratio; delay time (square planes with a distance d) L d 4 histogram (localized outgassing in square planes) L/d=1 Monte Carlo simulation of hitting times per molecule **localized outgassing Averaged hitting times, Or Maximum hitting times, is possibly useful for estimate the delay time. How does the N av (T delay ) increase as aspect ratio increases. number of molecules x= x=l/6 x=l/4 x=l/ hitting times per molecule

22 geometrical structure with high aspect ratio; delay time (parallel planes with a distance d) Averaged hitting times depends on aspect ratio, as a manner of (L/d) 2, (R/d) 2. L 1E+1 d 1E+9 uniform outgassing outgassing at x= 1E+8 R d Monte-Carlo simulation hitting times [averaged] 1E+7 1E+6 1E+5 1E+4 Can we derive 1E+3the hitting times from Diffusion Equation? 1E+2 1E+1 Monte-Carlo (square) D 2 p Monte-Carlo (circular) r 1 p q 2 ref., r r (L/d)^2 d p t Monte-Carlo (square) Monte-Carlo (circular) ref., (L/d)^2 1E+ 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 L/d, R/d L/d, R/d

23 geometrical structure with high aspect ratio; hitting times and delay time in Diffusion Equation Histogram corresponds to flow rate Q when outgassing of function occurs. N av time required for reaching R time required for a flight 4 histogram (localized outgassing in square planes) L/d=1 T delay ( /v) 2d; for spacing d 3 R d number of molecules 2 1 x= x=l/6 x=l/4 x=l/3 D 2 p r 1 2 r p r q d p, q (t ) t hitting times per molecule

24 geometrical structure with high aspect ratio; solving Diffusion Equation Green function for circular disks (infinite radius) p(r,t) G r,,t f ()d D 2 p f () ( ), at t r 1 2 r 2 6E-6 G 1 r r,,t exp 4Dt 4Dt 5E-6 pr,t 1 r2 4E-6 exp 4Dt 4Dt 3E-6 Qr,t AD p(r,t) r T av t Qdt / Qdt p, Q [arb] N av T av /( /v) 2E-6 1E-6 E+ p r t [sec] R p at 15m Q at 15m d q d p, q (t ) t R=15 m d=.4 m D=3 [m 2 s -1 ]

25 geometrical structure with high aspect ratio; hitting times derived from Diffusion Equation Green function for circular disks (infinite radius) R d N peak T peak ( /v) 3 32 T averaged t Qdt / 2 R d N av T averaged ( /v) diverging!!! T peak Q t Qdt diverging Although the peak shows an aspect ratio dependence of (R/d) 2, Green function for infinite radius is insufficient. Develop a Green function with appropriate boundary! hitting times [averaged] 1E+1 1E+9 1E+8 1E+7 1E+6 1E+5 1E+4 1E+3 1E+2 1E+1 outgassing at x= Monte-Carlo (square) Monte-Carlo (circular) ref., (L/d)^2 (3/32)(L/d)^2 1E+ 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 L/d, R/d

26 geometrical structure with high aspect ratio; solving Diffusion Equation Green function for tube (infinite length) p(x,t) G x,,t f ()d D 2 p f () ( ), at t x q 2 d p, q (t ) t 2 1 x,1 x,,t exp 2 Dt,9 4Dt,8 px,t 1 2 Dt exp x 2,7,6 4Dt G Qx,t AD p(x,t) x T av t Qdt / Qdt p, q [arb] N av T av /( /v),5,4,3,2,1 d L t [sec] x=l/2=15 m d=.4 m D=3 [m 2 s -1 ] p@3m q@3m

27 geometrical structure with high aspect ratio; hitting times derived from Diffusion Equation Green function for tube (infinite length) N av T averaged ( /v) L d 1E+5 d circular tube, L outgassing at x= L T averaged t Qdt / Qdt not diverging Although the averaged hitting times shows better agreement with MC plot, and an aspect ratio dependence of (R/d) 2, Green function for infinite length is insufficient at low aspect ratio. Develop a Green function with appropriate boundary! hitting times (averaged) 1E+4 1E+3 1E+2 (3/8)(L/d)^2 1E+1 Monte Carlo 1E+ 1E+ 1E+1 1E+2 1E+3 aspect ratio (L/d)

28 geometrical structure with high aspect ratio; hitting times derived from Diffusion Equation Green function for tube (infinite length) One of the possible correction for End effect L L* L N av T averaged ( /v) L * d corresponding to a Modified Green function G * (x,,t : L) () k G ( x,kl ( 2 3 )k,t) G x,,t 1 2 Dt diameter ( for tube) L*2 exp 4Dt 1E+5 1E+4 1E+3 1E+2 1E+1 End correction by a modified Green function is effective! hitting times (averaged) d L* circular tube, L outgassing at x= (3/8)(L*/d)^2 Monte Carlo 1E+ 1E+ 1E+1 1E+2 1E+3 aspect ratio (L*/d)

29 Vacuum System in Accelerator -- Geometrical structure effects on the pumping delay time -- Summary vacuum performance depends on the distribution of both outgassing rate and pumping configuration. *material surface treatment *optimizing pump configuration Geometrical structure effect is expressed as, SP=Q by matrix. pumping delay time can be estimated not only by Monte Carlo simulation, but also by solving Diffusion Equation. *hitting times per molecule *(L/d) 2 dependence *modified Green function R S 11 S n1 d O S ij O S 1n S nn N peak T peak ( /v) 3 32 P 1 Q* 1 M M P n Q* n 2 R d d L N av T averaged ( /v) L * d

30 3.11 disaster in KEK Fukushima Electr. Plant Tsukuba, KEK B, PF Tokyo Tokai, J-PARC

31 3.11 disaster in KEK My office, KEK, Tsukuba 7.5 GeV e-/e+ linac, Tsukuba J-PARC road, Tokai J-PARC ceramic chamber, Tokai