Cryogenic problems of forced cooled superconducting systems

Methods of producing cold compressed helium, various ways of refrigerant distribution and ways of reducing cool-down time being applied to forced cooled superconducting systems (FCSS) are discussed. The conditions obtained are for preventing normal zone progapation from current leads inwards into the winding. The analysis shows that main cryogenic problems of FCSS can be relatively simply solved.

Cryogenic problems of forced cooled superconducting systems V. E. Keilin and E. Yu. Klimenko

In our preceding paper I the advantages of forced cooled superconducting systems (FCSS) compared to conventional pool type superconducting magnet systems (SMS) were discussed and the main problems of FCSS were enumerated. In this paper various ways of solving the problems are discussed in more detail for the case of refrigerant flow inside the current-carrying conductor. Many of the solutions are valid not only for large FCSS but also for superconducting power lines. We do not consider here the case of so-called indirect cooling when helium is pumped through channels which are in some way formed into windings. The channels are discussed independently from the current-carrying conductor and therefore the case is easier hydrodynamically. Many of the solutions proposed are of course valid also for the case of indirect cooling.

The plan shown in Fig.1 was used in our laboratory to build a liquid helium installation with cold compressed helium output. FCSS for CERN's project 'Omega' is also provided with a cooling system capable of producing cold compressed helium. In this paper we shall not differentiate between hquefiers and refrigerators for the following reasons: 1. The design of liquefiers and refrigerators is almost equal. The difference is not in the methods of cold production but in the methods of cold utilization.

Production of cold compressed helium

VI

The continuous pumping of helium through channels of FCSS can be accomplished either with a pump for liquid helium 2 or with a refrigeration unit suitable for cooling down to working temperature a helium flow compressed by a normal compressor. 2 The latter method is in our opinion much more convenient as it can be realized by a slightly modified normal helium liquefier whereas the liquid helium pump is a rather eomptex mechanical device 2 with large heat losses due to the relatively high compressibility of liquid helium. The scheme for producing cold compressed helium is shown in Fig. 1. Most of the helium liquefiers (depending on their thermodynamic cycle) comprise throttling valve V1, liquid helium vessel 1, and a valve for liquid helium outflow. Adding to the scheme a valve V2 and a subcooler 2 makes it possible to feed FCSS with compressed helium at a temperature almost equal to that of vessel 1 (say, from I K up to 4.5 K). The valve V2 allows compressed helium pressure to be controlled in the range required up to the working pressure of the cooling cycle (typically, 15 + 25 atm).

LP L H e

The authors are w i t h the I V K u r c h a t o v A t o m i c Energy Institute, Moscow, USSR. Received 27 October 1971.

Fig.1 A scheme of cold compressed helium p r o d u c t i o n : 1 -- liquid helium vessel, 2 -- subcooler

292

- -

m

B

LHe

< V3

HP He yap

CRYOGENICS. AUGUST 1972

2. It seems that t o cool large FCSS combined liquefierrefrigerator installations are the most suitable: part of the cold is used in the refrigerative mode of operation at helium temperatures, say, to compensate for losses due to radiation, and the rest is used in the form of liquid helium whose vapour is utilized for cooling current leads and/or heavy supports (the case of complete utilization of helium vapour is equal thermodynamically to a refrigerator with many temperature levels). For example, in the CERN project of FCSS 3 a cold generator is provided, capable of producing 500 W at 4.5 K, 4 000 W at 90 K, and about 70 1 h -1 of liquid helium.

® Heleads

He yap =

;

|=

Heleods Refrigerant

distribution

"6

scheme

For FCSS under consideration long helium channels are typical, their length is equal to that of a conductor. For example, in the project mentioned 3 the total channel length is equal to about 12 kin. Various ways of refrigerant distribution along FCSS channels are possible. The simplest decision is to connect all the hydrafllical channels in series. We used that connexion in a small solenoid. 6 It obviates difficulties connected with the uneven distribution of helium flowing through several parallel sections and also eliminates the possible sharp reduction of helium flow through a section going normal. However series connexion initially results in a maximum pressure drop for a given system and secondly in this case some difficulties may arise with both current leads cooled with evaporated helium. It is more convenient practically to divide the helium flow into two or more parallel sections as is shown in Fig.2. Fig.2a corresponds to utilization of the whole evaporated helium to cool the current leads. The separation of hydraulical and electrical circuits can be provided with vacuum-tight non-conductive tubes 1. The scheme shown in Fig.2b corresponded to the case of partial utilization of evaporated helium for current cooling; the remaining part of of helium returns to the cold-generator at liquid helium temperatures. The proportion between lead cooling flow and refrigerative flow has to be chosen in each case depending on the relative importance of current heat influx. The number of sections is as a rule determined from cooldown time considerations.

(H~leads

He vap

® Fig.2 Methods of FCSS sectioning a -- two sections; b - four sections

He leads

When the pressure drop has no decisive importance and if the current conductor has several parallel channels, 2 a rather convenient scheme of helium distribution is possible, as shown in Fig.3. Half of the helium flow goes through one group of channels and half of the flow goes in the opposite direction. The flow leaving the channels can be conveniently used for current lead cooling. The scheme makes insignificant the uneven flow distribution because both hydraulical sections are thermally and electrically connected in parallel.

Q Heleads

When flowing along FCSS channels helium pressure is lowered and its temperature is slightly raised, in accordance with an isenthalpic curve (lab2 in Fig.4) in the enthropy S-temperature T diagram. In reality the curve of the process goes somewhat higher than the isenthalpic one due to heat influxes and Joule heating at electrical connexions on different sections of superconductor. Moreover, some temperature increase is possible due to compression type disturbances. 1

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Fig.3 Helium distribution in a multichannel FCSS with low pressu re drop

293

For superconductors with relatively low critical temperature, say for niobium-titanium alloy, even some tenths of a degree of temperature increase at 4 - 5 K may result in critical current reduction which is of the order of tens of percent. The greater the maximum magnetic field generated with FCSS, the more pronounced is the effect of critical current reduction. An effective way of preventing an excessive temperature increase in the winding is to use subcoolers (see Fig.5). Both entering the winding and between the different parts of the winding, helium is subcooled in the coils immersed into liquid helium.

T P/)

T~nox . . . .

P a ~,,.~

/

Pr,

Pi2

Trnox~ 1"o/I

d / f/

b

S

i=-

Fig.4 Temperature rise at isenthalpic helium flow

In the case of large FCSS the vessel 2 may be combined with the liquid helium vessel of the cold generator (2 in Fig.l). The subcoolers can be separated from an electrical circuit with vacuum-tight tubes, 3. The use of subcoolers avoids a significant temperature increase. If the pressures PI and P2 (see Fig.5) are the pressures of flow in the subcoolers then the isenthalpic expansion of the flow corresponds to a broken curve (lcdefgb2) with the maximum temperature significantly lower than in the first case. The intermediate pressures are determined mainly by practical considerations. The question about reasonable number of subcoolers is not quite clear. In CERN's project 3 the flow is subcooled after each pancake (12 subcoolers).

7

l _

The use of a subcooler is especially expedient for superconducting power lines. Some estimates show that at reasonable value of initial pressure P, helium can be transported through a tube as long as 1 000 km, provided heat influxes are compensated in subcooling stations with a distance between them of the order of 100 km. An additional advantage of subcoolers is the possibility of using them for stopping the process of thermal propagation of a normal zone along the winding. It should be noted that in general in the case of FCSS their protection under superconducting-to-normal transition is rather favourable. Firstly, the presence of a narrow reversible portion on the current-voltage curve of FCSS allows for well-timed detection of a normal zone. Secondly, even if the protective measures to limit or to lower coil current are not undertaken in time, the stored energy of FCSS is dissipated in the main part of the winding. This is due to finite cooling capacity of helium flow which results in rather high velocity of normal zone propagation. At the same time the emergence of high electrical voltages in FCSS is not probable because of rather large normal-tosuperconductor ratio in the current-carrying conductor.

Cool-down

of FCSS

Cool-down of FCSS is defined by one of the three considerations: 1. thermal stresses, 2. cooling capacity of a cold generator, 3. flow limitations due to pressure drop. Because of the large degree of temperature nonhomogeneity during cool-down, thermal stresses impose a rather serious problem. However a preliminary analysis

294

2

Fig.5 Methodof subcoolersintroduction: 1-- subcoolers, 2 - liquid helium vessel

shows that using relatively simple designs, thermal stresses can be considerably lowered. It should be noted that thermal stresses may limit not only cool-down velocity but also warming-up one. The thermal stresses problem is worthy of more detailed study, though preliminary estimations show that a model of cool-down process proposed in reference 3 which leads to a long (about 200 hours) cool-down period is unlikely to be valid. The cooling capacity may as a rule limit the cool-down velocity only at sufficiently low temperatures. Moreover, this limitation can be easily eliminated using liquid helium from an outer store. This additional liquid helium can be supplied, say, into the liquid helium vessel of the cold generator. Additional liquid helium can be also used to prolong the working time of FCSS when the cold generator has to be repaired. Subcoolers can also be used for this purpose. Let us enumerate in more detail the ways of shortening the cool-down period, provided its velocity is defined by pressure drop. It can be easily seen that the subcoolers mentioned above can be effectively used to shorten cooldown period. The effective method at the early stage of cool-down is to fill the subcoolers with liquid nitrogen. It is possible also to switch sections of FCSS from series connexion to a parallel one. 3 However, this method demands a great number of cold valves. In our opinion it is

CRYOGENICS. AUGUST1972

simpler to use method shown in Fig.5. Warm valves V1, V2 and so on at early stages of cool-down are open. Therefore the refrigerant flows mainly only in the first section. After it is sufficiently cooled the valve V1 is closed and so on. The same offsets can be used for safety valves. It was shown in our paper 7 that cool-down of FCSS can be accomplished with an amount of refrigerant close to the theoretical minimum (if only the turns of FCSS are not in intimate thermal contact). The conclusion was that for such systems the use of liquid nitrogen in cool-down procedure is not of prime importance. Current leads

The necessity of lowering the pressure drop and the number of parallel sections of FCSS is equivalent to increasing the total cross-section of current-carrying elements and decreasing their length. In other words, for FCSS large currents are typical. To lower heat influx through current leads it is expedient to use a considerable portion of helium to cool current leads. In Fig.6 a scheme is shown which corresponds to using all the evaporated helium to cool the leads - from the channels of the FCSS itself and also from the subcoolers. According to the scheme helium from FCSS channels enters the subcoolers and all the gaseous

helium from the subcoolers leaves the system through heat exchangers in the current leads. The scheme is simultaneously valid for balancing the capacity of cold generator and the heat inputs to FCSS. Namely, it is possible to feed FCSS with helium mass flow slightly higher than is necessary to compensate heat inputs. The excess of liquid helium will separate in the subcoolers. In connexion with large working currents of FCSS there is a danger of normal zone propagation from a lead into a winding. Let us consider this problem in more detail. The model of the process is shown in Fig.6. The heat conduction equation for a superconductive part of the lead (T < Tc, where Tc - critical temperature at a given value of working current D is

cm dT

d2T dx 2

+

aS dx

-0

(1)

where m = mass flow of refrigerant, and X, S - heat conductivity and cross-section of the lead, respectively. The heat input Q to the point C is practically independent of the value of Tc (as Th >>Tc and Tc is of order To). Therefore Q can be found (see reference 8)

dT)

Q =-~cS

Th

~-

I2pX

c ~cM

Here Xc and S correspond to T < Tc; ~- and X are average values of electrical resistivity and heat conductivity of lead material at T > Tc, ~ is a factor, which allows for a degree of utilization of evaporated helium and c andM are specific heat and total mass flow of refrigerant (see reference 8 for more detail). So if we know S(dT/dX)c and Tc (1) can be easily solved. Its solution at x + oo goes to To. This results in a condition of thermal stability:

1~

Tc-r o

Tco(flcM) (cm)

Tco

(2)

Here Tco is the critical temperature in a given magnetic field when I = 0. It can be approximately written

o -Io uo "l-

z.

Tc

I

~o

4

(3)

where Ic is the critical current at T = 0 in a given magnetic field. Taking into account the definitions

3E

a =

7Co (/3cM')(cm)

;

./-

Ic

;

Tco

- v0

(3) and (2) can be rewritten Fig.6 Derivation of stability conditions f r o m lead-toc o n d u c t o r normal zone propagation

C R Y O G E N I C S . A U G U S T 1972

o~] <~ 1 - ] -

vo

(2a)

295

Its solution corresponds to the limiting stable values of current where the normal zone does not propagate into the winding

( vo) --+

(4)

4¢z2 or approximately

/ ~< (1 - Vo) [I - (1 - Vo) ix]

(4a)

It can be seen that stable values of a current are considerably lower than the critical current. Therefore additional measures have to be undertaken to stabilize the transition portion of the lead. These measures are 1. A local increasing of superconductor cross-section; 2. An additional cooling of the transition portion, including its possible cooling by immersion in a liquid helium bath.

Conclusions The analysis confirms that the main cryogenic problems of FCSS can be solved with relative simplicity. The typical feature of these solutions is the possibility of a complex usage of different elements of a system.

296

The considerations given above show that the larger superconducting magnet systems the more complex the problems to be solved. The question is quite different with FCSS. The larger FCSS the simpler (relatively, of course) some problems can be solved, as certain complications of the scheme become more justified. Therefore it can be expected that starting with sufficiently large systems the maintenance of FCSS will become even simpler than that of traditional systems. The authors are deeply indebted to B. N. Samilov, N. A. Chernoplekov, and I. A. Kovalev for numerous fruitful discussions.

References 1 Keilin, V. E., Klimenko, E. Yu., Kovalev, 1. A., Samoilov, B. N. Cryogenics 10 (1970) 224

2 Morpurgo, M. 'Construction of a superconducting test coil cooled by helium forced circulation', CERN 68-17, Geneva, 1968 3 Morpurgo, M. ParticleAccelerators 1 (1970) 225 4 Keilin, V. E., Klimenko, E. Yu., Kovalev, I. A. Cryogenics 9 (1969) 100 5 Depierr¢, Y., et aL Paper E-7 Commission I or IIR, Kyoto, Sept 1970 6 Agureev, V. N., Keilin, V. E., Klimenko, E. Yu., Sarnoilov, B. N. Cryogenics 9 (1969) 26 7 Keilin, V. E., Klimenko, E. Yu., Oshogina, V. C. Cryogenics

(forthcoming) 8 Keilin, V. E., Klimenko, E. Yu. Cryogenics6 (1966) 222

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