TF 线圈分流温度推算

Non-Cu critical current densities in NbTi and Nb3Sn type of wires

Critical current measurement ( 运行电流和临界电流 )

Measurement Tcs of TF

运行温度，分流温度和温度裕度

ITER 设计中运行条件：

1) As an overall stability margin a temperature margin, expressed as the difference between the maximum operating temperature Top and the associated current sharing temperature Tcs,

should not be less than 1K for Nb3Sn and 1.5K for NbTi.

2) Iop < Ilim = (p h ACu (Tc-Tb)/) 0.5

ITER 设计中考虑的磁体热负荷主要有

Nuclear Heating, Thermal Radiation and Thermal Conduction through Supports ， AC Losses and Eddy Currents

ITER的热负荷

EAST 同样也有各种热负荷，所以也必须要有温度裕度

EAST TF 导体设计参数

温度裕度 1.88K @4.2K,5.8T,14.3kA极限电流 Ilim = 18.1/10 kA稳定性裕度 ΔE = 250 mj/cm3

Results: Eddy Current Heat dissipation on Cases

0 20 40 60 80 100

0

2

4

6

8

10

Total: 212 kJ

Eddy

Heatin

g R

ate

s o

n T

F C

ases (

MW

)

Time (ms)

条件 :1.5MA等离子体在 3ms破裂

Results: Case Temperature Evolution

• Tmax: 19 K• Recover

Time:

3 min.

Results: Case Coolant Temperature Evolution

• Tmax: 8.9K

The temperature rise of the coolant in CICC of the inner corner turn due to case heating under plasma disruption.

线圈盒涡流对邻近导体中氦流温度的影响

Peak temperatures of TF case and coolants

case Case coolant He in CICC

Tmax 19.4 8.8 4.4

Occur time(s) 0.07 2 10-15

position Middle of inner straight leg

~Middle of inner straight leg

~Middle of inner straight leg

Recover time

3 min

Integration of d2Bn/dt2 over 50 ms after plasma disruption,

half of straight leg lasts 0.917 m.

等离子体破裂时纵场导体中的偶合损耗计算

GANDALF Modeling

• SC properties: – Tcs: 5.83 K, Jc: 71% of theoretical value

• Coupling loss

– coupling time constant : 37 ms

• Cables modeled: inner corner turn, ~ 10 m

• Results: Temperature margin reduced: 0.63 K

2

2

0

2

dt

Bdq n

Summary

• Most of the eddy heating on cases occurred on the inner straight leg, causing case temperature rise to 19 K

• Eddy heating on cases can heat up LHe in winding pack to 4.4 K at 15 s, reducing temperature margin by 0.4 K, but before 2s, the rise is less than 0.1 K

• Coupling loss reduces temp. margin by 0.63 K– Temperature margin still have: 1.3 K ( Top=3.8 K)

• After a major centered disruption, the case can be recovered within ~3 minutes

线圈盒冷却对绕组的影响

肖炳甲2004/11/30

线圈盒采用 4.5K 的冷却，高于线圈的 3.8K

初略估计： q=kAT/d~60 W/ 每 TF 线圈 共 > 1000 W

结论：•如采用 4.5K/3.8K 的冷却线圈盒 / 线圈，线圈的冷却温度（出口）实际为 4.1 K•考虑到实际情况 , 线圈盒温度以及线圈盒上的氦温度可能比 4.5 K 要高，绕组的工作温度将进一步升高，高等离子体电流运行时，绕组将相当危险，需要对此引起足够的重视•建议线圈盒 / 线圈都采用同一温度冷却，例如 4.0 K

ASIPP

0 to 15.2 kA (1 kA/s)flat top 20 s15.2 kA to 12kA （– 20 kA/s, 160 ms)12 kA to 10.6 kA –（ 10 kA/s, 140ms)10.6 kA to 6.6 kA （ -5 kA/s ，0.8 s) 6.6 kA to –13.2 kA （ -1.5 kA/s flat top 10 s–13.2 kA to 0 (3KA/s ). T 0.5 K

Simulate Plasma initiation

ASIPP

PFMC test

Simulate Plasma initiation

陈灼民根据线圈失超实验推算的 TF线圈外推性能一览

找出性能最差的线圈 TF10 ＃，根据其失超参数12.04kA@7.89K/1.6976T ，按照公式：

先计算出其在任意工作电流下的临界电流；

再按照公式 :

00

0 0

1 0.096*( , ) * (1 )

1 0.096*C CC

T TBI T B I

B T T

)/1)(( copopcopcs IITTTT

根据临界电流计算结果即可推导出其在不同工作温度下的分流温度。

Iop Tcs 3.8K

 4.2K

 4.5K

 5.0K

 5.5K

 6.0K

1kA 8.99293 8.99247 8.99207 8.99125 8.99016 8.98864

2kA 8.78278 8.78213 8.78155 8.78038 8.77883 8.77666

3kA 8.56937 8.56883 8.56835 8.56738 8.56608 8.56427

4kA 8.35251 8.35243 8.35235 8.3522 8.35201 8.35174

5kA 8.13195 8.13275 8.13344 8.13486 8.13675 8.13938

6kA 7.90746 7.90961 7.9115 7.91536 7.92048 7.92761

7kA 7.67874 7.68282 7.6864 7.69372 7.70344 7.71696

8kA 7.44545 7.45213 7.45801 7.47001 7.48594 7.50811

9kA 7.20721 7.21731 7.22619 7.24434 7.26842 7.30194

10kA 6.96354 6.97805 6.99081 7.01687 7.05146 7.0996

11kA 6.7139 6.73402 6.75172 6.78785 6.83582 6.90258

12kA 6.45762 6.48484 6.50879 6.55768 6.62258 6.7129

13kA 6.19386 6.23006 6.26189 6.3269 6.41319 6.53329

14kA 5.92156 5.96911 6.01093 6.09634 6.20972 6.3675

14.3kA 5.838 5.88953 5.93485 6.02739 6.15024 6.3212

15kA 5.63932 5.70133 5.75587 5.86724 6.01509 6.22084

16kA 5.34529 5.42587 5.49675 5.64147 5.8336 6.10097

16.4kA 5.22382 5.3133 5.392 5.5527 5.76603 6.06292

17kA 5.03684 5.14161 5.23376 5.42193 5.67173 6.01938

分流温度推算结果

ASIPP

Tcs VS field

瑞士导体短样测试结果 TF:Tcs @ 5.8T,14.3 kA

需要说明的问题

对于大杜瓦实验，其失超保护电压为 50mv ，（相当于有 0.9 米导体失超）远高于临界电流的判据 0.1 ，因此测量出来的实际上是失超电流而不是临界电流，因而由此推算出来的分流温度偏高一些。最近在测试 ITER 导线时发现西北院和俄罗斯股线在临界条件下性能下降 , 即温度裕度小于按公式计算值 .

根据肖柄甲对线圈盒冷却及线圈盒对线圈传热的计算线圈上的局部最高温度可能会高于进，出口温度。

cmv /

ITER requirement Impact of the Jc scaling. Three Jc(B,T) scalings are compared below: (1) the Jc scaling described in apxC of FDR98 and used for the PF conductor design in both BDPA-2000 and DDD-2001, (2) the nbti Jc scaling based on the fit proposed by L. Bottura and described in DRG1 MS&EDCRITERIA - 2001 and (3) a fit derived by E. Zapretilina from measurements carried out on the RF nbti strand for the PF insert. The 3 of them are adjusted to give the same reference value of 2900 A/mm2 at 5T, 4.2K. The figure below shows the ratio (2) to (1) and (3) to (1) . One can notice the large discrepancy at high field - high temperature with the Jc fit derived from the measurements of the RF nbti strand for the PFI.

ITER requirement

DB 15.10.2005 NbTi Jc  Jc data from various sources are plotted in the 3 figures below. Actually these are fits to data except the values related to the RF strand. Those data and the related fits were generally presented at ITER meetings during the past 3-4 years. Although the Jc requirement of 2900A/mm2 at 5T and 4.2K is broadly achieved, the Jc values at the design condition of the PF conductor (Top + Tmarg = 6.5K) are below the design requirements when using the L. Bottura fit as recommended in the ITER design criteria. The Jc requirements related to operation of the PF conductor in normal mode can be defined as follows:At 4T, 6.5K 985 A/mm2At 5T, 6.5K 560 A/mm2At 6T, 6.5K 185 A/mm2Strands with a high dJc/dT seem to perform better at 4.2K, whereas a lower slope gives apparently higher performance at 6.5K suggesting that some potential for improvement exist.The main question remains: to what extent the nbti strands could be optimised to achieve the required Jc at 6.5K, relaxing the 4.2K requirement if necessary?

Based on the presently available database, a consistent design of the PF conductor could be performed if we accept a reduction of the 1.5K temperature margin (1.2 – 1.3K seems ok).

4 4.5 5 5.5 6 6.5 70

0.5

1

1.5

2

2.5

3

3.5x 10

9

Temperature (K)

Jc (

A/m

2

Jc NbTi B=5T

crpp - A13 Cada Mar2001crpp - B6 Cada Mar2001crpp - B910 Cada Mar2001crpp - C12 Cada Mar2001TwenteCEA - Alstom SSampleCEA - EM LMI SSampleJCT apx-C (2000)IT LB fit (2001)crpp - A Gstadt Jan2003crpp - B Gstadt Jan2003crpp - C Gstadt Jan2003RF PFI 2001 (memo #8)RF PFI 2003 (memo #8)

几点建议：•在降温过程中设法对温度计显示值（根据超导转变温度） 进行修正•线圈进出口温度差控制在小于 0.5K•注意监测线圈盒及极向场支撑的温度，并使线圈盒温度 和线圈进出口温度之间的温差尽量小，•用线圈进出口温度的最大值加 1.5 K 的温度裕度来选取 工作电流 .•注意对未经实验（ PF11-14)以及未经充分实验的中心 螺管线圈的监测和实验，建议根据冷却情况，及时组织 对上部 PF线圈实验内容的讨论 .•争取试验一下降压过冷 (3.8K)的冷却模式 (按肖炳甲的计算 此时线圈上靠近线圈盒的温度为 4.1K)•选用较低的失超保护门槛值 ,如 50 毫伏