some aspects of the layout and optimization for the ... · some aspects of the layout and...

Some aspects of the layout and optimization for the cryogenic

supply of superconducting linacs

ERL2005 Workshop, Jefferson Lab,Va,USA, March 19-23,2005

Working Group 3

Bernd Petersen DESY, Hamburg, Germany

ERL2005 Bernd Petersen DESY

Overview• Introduction• High Q-Cavities Q = Q(T)• 2 K principle cooling scheme• Helium plant coefficient of performance COP = COP (T)• Cold Compressors• HeII Parameters = f(T)• Critical gas flow conditions = f (T)• Kapitza thermal resistance = f (T)• European XFEL-Linac as an example• Cryoplant parameters = f(T)• Conclusions


Introduction

ERL superconducting linacs will dissipate power

in the order of some kW at temperatures < 2.17 K

In view of conversion factors to primary power consumption

in the order of 1000 = primary power / load at low temperatures

it seems to be worth while to try some optimization


Introduction (cont.)

My talk is restricted to SL-linacs operated around 1.3 – 1.5 GHz

and to liquid helium II bath cooling below 2.17 K

The optimization is focused on the T< 2.17 K cooling circuit

( the 5-8 K / 40-80 K thermal shield niveaus are not discussed )The discussion is coupled to the believe that we can assume a

BCS Q = Q (t) dependence and the temperature dependent dynamicloads are dominating

DISCLAIMER:

Some XFEL-parameters, which are shown here, are in no way ‚official‘ project parameters. Often ‚hand-waving‘ argumentation isused to get qualitative results. Do not base the design of yourmachine on these data !


High Q Cavities

About factor 2 dynamic load reduction at 0.2 K temperature

reduction below 2.17 K !

1.00E+09

1.00E+10

1.00E+11

0 10 20 30 40

Eacc [MV/m]

Q0

2 K

1,8 K

1,6 K

1011

109

1010

AC70 1.3GHz 9-cell,TESLA-cavity

BCS T-dependence at medium fields


High Q requries proper magnetic field shielding !

AC70 result achieved by reduction of earth magnetic field to about 3 %

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sensor position [m]

|B| [

G]

middlebottomtopLeftright

view from big s ide

natural field niveau: 0.25…0.3G

sm al s ide big s ide

Measurement of cryoperm magnetic shielding in horizontal cryostat


Q (T) is linked to the BCS surface resistance

Rs = A f2 exp –∆/kT (+ R0)


Diagramm taken from:

1.5 K is taken here as a reasonable lower limit of BCS Q=Q(T) dependence

Rs : BCS surface resistance ∆ : BCS energy gap A : material constant k : Boltzmann constantf : frequency T : temperature

R0: residual resistance

RS [nΏ]

TD-04-014, June 2004

2K Cooling Scheme ( simplified)

0.5 bar T cc out

Cold Compressors

P cc in T cc in

T bath = f ( P bath )

P bath

4.5 K load

40/80 K load

PrimaryPrimary PowerPower

HEX

HEX

HEX

HEX

JT


Coefficient of PerformanceCOP vs T

0200400600800

10001200

0 10 20 30 40Temperature [K]

CO

P

COP at Low T

0200400600800

10001200

1.5 1.7 1.9 2.1

Temperature [K]

CO

P

measured LHC value at 1.8 K

COP=1/( K * η CARNOT)

η CARNOT = T/(300 -T)

K= 0.176 ( from latest LHC measurements at 1.8 K)

COP= Primary Power/ Power at TT

TMR

JLab


Power Consumption

Refriger-ation

COP

W / W

Specific Load

% of Power

2 K 4.3 kW 588 2500 kW 49 %

5 – 8 K 7.5 kW 168 1254 kW 24 %

40 – 80 K 80.8 kW 17 1373 kW 27 %

Total 5147 kW 100 %

Power Consumption of the TESLA Model RefrigeratorExample for the required power at different T levels


Cold Compressor Cartridges of 2.4 kW @ 1.8 K Refrigeration Units


Cold compressor impellerIHI-Linde

The four-stage LHC cold compressors1st stage

Example of a cold compressorwith active magnetic bearingsused at Tore Supra, CEBAF and Oak Ridge


Development of the Efficiency of Cold

Compressors

Tem

pera

ture

(T)

Entropy (s)

P1

P2

1

2

2'

0

10

20

30

40

50

60

70

80

1985 1993 2000Year of construction

Isen

tropi

c ef

ficie

ncy

[%]

Tore SupraCEBAF

LHC

12

12'is HH

HHη−−

=


Cold Compressor Parameters

Insentropic efficiency of 0.7 assumed

Maximum compression ratio per single CC around 3 !


TEMP K

PRESS Pa

ENTROPY J/gK

ENTHALPY J/g

XFEL MASS FLOW g/s

KOMPRESSIONPOWER W

XFEL cw MASS FLOW g/s

KOMPRESSIONPOWER W

1.6 746 14.49 23.32

4 746 19.36 36.01

21.53 50000 19.36 126.8

28.99 50000 20.91 165.71 26.7 3462.99 135 17509.5

1.8 1638 13.43 24.2

4 1638 17.72 35.96

15.73 50000 17.72 96.54

20.7 50000 19.15 122.5 34.8 3011.592 264 22846.56

2 3129 12.58 25.04

4 3129 16.36 35.88

12.14 50000 16.36 77.7

15.56 50000 17.66 95.62 48 2867.52 466 27838.84

Helium II parameters = f(T)

Helium Parameters vs. Temperature

0

5

10

15

20

25

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2

Temperature [K]

Hea

t of V

apor

isat

ion

[J/g

] / J

T Q

ual %

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Vapo

r Pr

essu

re [b

ar]

Heat of vaporisation

JT-Quality %

Vapor pressure

-> more mass flow needed at LT


Helium II parameters = f(T) (cont.)-> Cooling instable below 1.8 K ? Test required !

Lambda, Cp,Diffusivity,Density of HEII

0

2000

4000

6000

8000

10000

12000

14000

16000

1 1.2 1.4 1.6 1.8 2 2.2

Temperature [K]

Lam

bda

[W/m

2], C

p [J

/kg]

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Diff

usiv

ity [m

/s]

Lambda max in a saturated bath

Cp of liquid

'Diffusivity' = Lambda/(RHO*Cp) [m/s]

Liquid density=RHO [kg/m3]


Definition of Lambda max in a HEII bath

Heat conductivity in HeII q**m = f(T) * dT/dxT-Temperature, x-lengthm ≈ 3

f(T) Germany = f**(-1) (T) USAT2

q max * L** 1/3 = [ ∫ f(T) dT ]**1/3 T1

T1 = F ( P1 ) Temperature function of vapour pressureT2 = F ( P1 + ∆ P ) ∆ P = ρ*L*g ρ= density of liquid g=9.81 m/s2

L= depth in bath

T1, P1 at liquid surface

T2 must not beexceeded to avoidbubbles !T2, P2 at depth L in the bath

L



2.2 K forward

5 K forward

40 K forward

2 K 2-phase

cavity

2 K return

80 K return

8 K return

cool down/warmup

support

coupler

300 mm

XFEL-Cryomodule

2-phase flow

involved

2-phase flow characteristics for XFEL-Cryomodules

Flow pattern map for He II - vapor flow in the two-phase tube of 7 strings of TESLA XFEL (12,5 W / cryomodule)

1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

He II level / Tube diameter

K

Stratified Smooth - Wavy (K)

SSW_K (string 1)

SSW_K (string 4)

SSW_K (string 7)

( ) ( )βµρρρρ

cos

2

⋅⋅⋅−⋅⋅⋅

=LGL

LSGSGL

gUUK

Stratified Smooth

Stratified Wavy

TubeL

LLS A

mU⋅

=ρ

& TubeG

GGS A

mU⋅

=ρ

&


2-phase flow characteristics for XFEL-Cryomodules- > Lower densities balanced by smaller flows ?

K Values = f (T,m)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

1 1.2 1.4 1.6 1.8 2 2.2

Temperature [K]

K-V

alue

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

Gas

Den

sity

[kg/

m3]

Transition to wavy

4.8 g/s string mass flow for Q ( 2 K)

3.5 g/s string mass flow for Q ( 1.8 K)

2.7 g/s for Q(1.6 K)

Simplified dependencies : K ~ mG sqrt ( mL / ρL* ρG)

Density


Kapitza Heat Transfer-> Seems to be no limit under reasonable boundary conditions

0

50

100

150

200

250

300

350

400

1.5 1.7 1.9 2.1

Temperature [K]

Dis

sipa

ted

Hea

t [W

]

0

0.1

0.2

0.3

0.4

0.5

0.6

Kap

itza

Res

ista

nce

[W/K

*cm

2]

Hk=0.043*T**3.18 W/K*cm2

Heat transfer at the surface of oneTESLA cavity ∆ T = 100 mK


XFEL-Accelerator schematic layout

0.4

km1.

7 km

BC-I

BC-II

CollimationDiagnostics

Beam distr.

0.5GeV

10…20GeV (-->25GeV)

2 GeV

LINAC

Injector

beam lines

120 modules30 RF stations

Main linac Beam energy 20 GeV acc gradient 22.9 MV/m Bunch spacing 200 ns beam current 5 mA power beam p. klystron 3.8 MW incl. 10% + 15% overhead 4.8 MW matched Qext 4.6⋅106 RF pulse 1.37 ms Beam pulse 0.65 ms # bunches p. pulse 3250 Rep. rate 10 Hz Av. Beam power 650 kW


Site near DESY laboratory


3.2km


Wavelength vs. acc gradient

Photon wavelength vs E_acc, reference point 1 Angstroem at 17.5 GeV

00.20.4

0.60.8

11.2

1.41.6

15 17 19 21 23 25 27 29

E_acc [MV/m]

Lam

bda

[Ang

stro

em]

25 GeV17.5 GeV

Nominal linac energy 20 GeV, includes 57Fe line @ 0.8ÅExpected better cavity performance permits higher

energy/smaller wavelength

20 GeV XFEL parameters 10 Hz650 µs Pulse 23.5 MV/m

0

500

1000

1500

2000

2500

3000

3500

1 10 19 28 37 46 55 64 73 82 91 100 109 118Length [Cryomodules]

Vapo

r Pre

ssur

e [P

a]

0

0.0050.01

0.0150.02

0.025

0.030.035

0.040.045

0.05

Hel

ium

Mas

s Fl

ow ◘

kg/s○2K 1016 W

1.8 K 708 W

1.6 K 520 W

2K 48 g/s1.8 K 34.8 g/s

1.6 K 26.7 g/s


XFEL ERL-up-grade ?

0

500

1000

1500

2000

2500

3000

3500

1 9 17 25 33 41 49 57 65 73 81 89 97 105 113

Length of Linac [Cryomodules]

Vapo

r -Pr

essu

re [P

a]

0

0.1

0.2

0.3

0.4

0.5

0.6

Mas

s Fl

ow [k

g/s]

1.8K 5.373 KW

2K 10 KW

1.6K 2.618 KW

15 MV/m duty=0.5 Q=Q(T)

Q=Q(T)

mass flows

vapor pressure

vapor pressure

vapor pressure


All in one – the lower the better !?


0

200

400

600

800

1000

1200

1400

1600

1800

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2

Temperature [K]

Prim

ary

Pow

er [W

]

0

0.5

1

1.5

2

2.5

Pow

er a

t Low

Tem

p [W

]

COP

CC

Work of compression * mass flow

COP + explicit CC

1 W dynamic

+1/3 W static (XFEL)

Conclusions

• Lowering the temperature seems to be effective as long as Q = Q(T) follows BCS and the temperature dependent dynamic loads dominate ( reasonable lower limit 1.5 K)

• Watch the temperature independent loads: HOMs, couplers…, static• The long term stability of the Q = Q(T) characteristic has to be proven• HeII cooling might become unstable below 1.8 K – tests required• Another cold compressor stage is required for each 0.2 K temperature step to lower

temperatures – investment costs and system complexity increase• In view of pressure drops, critical gas velocities, work of compression and general

sizing the lower gas densities at lower temperatures seem to be balanced by thelower cooling loads and the related lower mass flows

• If the cryogenic layout is suited for 2 K operation, it should also allow operation at lower temperatures as long as Q = (T) works ( beside the necessity of more CC stages) – for the time beeing this is our baseline for the XFEL


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