QM-001-Tempstudy1

Temperature Behaviour of the QM-001 Quadrupole Magnet (Everson Tesla Quad)

Achim W. Weidemann ----------------- Draft of 22 December 2005

Introduction

In this memo/webpage, I summarize the temperature studies of that magnet (Serial Number 001, SLAC-PO # 56486).
The aim is to find if this magnet can operate without overheating in a way as to generate an integrated field strength of
as much as 3 Tesla, or at least 2.5 or 2 Tesla [1].
Mesurements of the coil surface temperature are consistent, but apparently higher in value than those calculated as 'average' or 'hottest' temperatures inside the coil. This is still a puzzle.

Required currents

The currents required to produce the desired integrated field were determined, by bucking-coil measurement,
to be as shown in this table:

Measured Int. Field [T]:	3.0075	2.504	2.0005
Measured Current [A]:	20.591	15.475	12.20
RT Data Sets	.r21 (4h)	.r27(4h),r33(8h)	.r32(6h)

(The last line lists the data sets taken, for my own memory.)
Integrated field strengths for several other currents are also available.

Measurement Setup

Three temperature probes were read out; the first one was affixed to upper coil on the side with the connectors in
about the middle of the coil, just below the klyxon thermocouple; the second one at the same location on the top coil
away from the connectors; a third one was lying on the measurement table to measure the ambient air temperature.
Temperatures were read every minute.

Figure 1 above shows a typical temperature measurement; the wiggles in black curve for the first sensor indicate
that apparently it does not make good thermal contact witht the coil; therefore in the following, I only use
the second sensor.

Fits to Coil Surface Temperatures

The Temperature vs Time curves were fitted to a function of the form:
T_init + alpha*(1 - exp(-beta*t ), form, where T_init is the first temperature measurement.
using MathLab [3] From these fits, one can deduce the asymptotic outside temperature,
      T_asym = alpha+ T_init,
and a time constant,
   timec = 1 / beta.
The figures below shows such fits (where T_init has been subtracted), and the residuals (data-fit).

(Right-click on a figure and 'Open Link in New Tab' for a clearer view of any figure)

(r21: 4h,3T)	(r27: 4h, 2.5 T)
(r32: 6h, 2T)	(r33: 8h, 2.5T)

The fit results are summarized in the following table:

Datafile (rtplt...)	r21	r27	r33	r32
Int. Strength [T]	3	2.5	2.5	2.0
Current [A]	20.59	15.47	15.47	12.20
Lenght of measurement [h]	4	4	8	6
Ambient Temperature at end [deg C]	20.56	22.67	24.58	23.79
Last measured Temperature [deg C]	64.6	48.5	50.3	40.9
Asympt. Temperature [deg C]	64.4	48.1	49.8	40.7
Time Constant [minutes]	57.5	53.3	60.4	66.7

So one may conclude that the time constant of this magnet is about one hour.
The asymptotic values are close to the values measured last, and the difference between
the 4 and 8-hour measurement at 15.47 A can be explained by the difference in ambient
temperature.--

Resistance Temperature Study

The above dealt only with consideration of the temperature as measured at the surface of the coil.
However, the SLAC Solid Coil Cooling Reqirements [2] relate to the temperature inside the coil,
which can be deduced from a measurement of the resistance R at the given temperature after thermal
equilibrium, presumably at least 6 hours, and the resistance R0 at low current at room temperature.

An average coil temperature is then      T_ave= ( R- R0 )/(R0*0.00393) + T_room, (1)
the coil surface temperature and resistance is measured until the coil voltage does not increase any more.
The the 'hottest' temperature in the coil is

                         T_hottest =   2* T_ave - T_surface
                         (which derives from T_ave =   (T_hottest + T_surface)/2 ).
The requirement is then that this hottest temperature is below 100 deg C at all times,
also considering that the ambient temperature in an accelerator enclosure may be quite high (35 deg C).
The coil current and resistance are already measured in the standard setup.

In a separate run (.r39) I measured a resistance of 434.8057 mOhm for the coil (as avearage of 9
measurements at 0.27 and 0.446 A, ignoring one outlier ,485 mOhm), with coil temperatures
at the surface of 23.86, 23.97 deg C, and ambient temperature 23.54 deg C.
I repeated this (at 0.26 A) and found a similar result.

However this value may be wrong, as the results indicate a 'hottest' temperature
less than the asymptotic value for the coil surface temperature,
as shown in the last two rows of this table:

Datafile (rtplt...)	r21	r27	r33	r32
Int. Strength [T]	3	2.5	2.5	2.0
Current [A]	20.59	15.47	15.47	12.20
Lenght of measurement [h]	4	4	8	6
Ambient Temperature at end [deg C]	20.56	22.67	24.58	23.79
Last measured Temperature [deg C]	64.6	48.5	50.3	40.9
Asympt. Temperature [deg C]	64.4	48.1	49.8	40.7

T_ave [deg C]	58.7	46.1	50.1	40.1
T_Hottest [deg C]	52.6	43.7	49.8	39.4

This result does not differ much if the final resistance measurement is taken as such, or as the maximal R measured, or the asymptotic value from a fit. Perhaps this indicates that -either the result for R0 is wrong
or that indeed thermal equilibrium had not been achieved.

Plotting the difference of subsequent voltage measurements, one has the following:

(Right-click on a figure and 'Open Link in New Tab' for a clearer view of any figure)

(r21: 4h,3T)	(r27: 4h, 2.5 T)
(r32: 6h, 2T)	(r33: 8h, 2.5T)

(Horizontal Scale: Time [minutes], VerticalScale: Voltage [V}).
So in all cases the remaining fluctuations in voltage are small, below 2mV; but for the 4-hour measurements, there still is a small trend (differences all positive) I also plotted the 'hottest' temperature as calculated above as a function of time (taking as R in (1) the value measured at that time). (Right-click on a figure and 'Open Link in New Tab' for a clearer view of any figure)

(r21: 4h,3T)	(r27: 4h, 2.5 T)
(r32: 6h, 2T)	(r33: 8h, 2.5T)

(Black-lower curve: 'Hottest Temperature'; Blue-upper curve: Surface Temperature). One would alsways expect the surface temperature to be lower than the 'hottest,' but this seems not to be the case here.
In the new year, I plan to separately measure the coil resistance with a Milliohmmeter or similar device. Here the voltage measurement is done at the output of power supply; not at the magnet leads; as only a resistance difference (R-R0) goes into temperature calculation (1), this sould not make any difference. Nevertheless is would be good to have an independent resistance measurement.
Any other suggestion is welcome!

References

1. Charge (R. Carr e-mail of Nov. 21, 2005)
2. Cherrill Spencer, SLAC's Magnet Coil Cooling Requirements for Air Cooled Coils. Memo of 20 Dec 2005 [MS-Word .doc]
3. MathLab code for generating the above fits and figures: rtanalysis.m