inductance and magnetization measurements on main dipoles in sm18 emmanuele ravaioli thanks to a....

Inductance and magnetization measurements

on main dipoles in SM18

Emmanuele Ravaioli

Thanks to A. Verweij, S. Le Naour

TE-MPE-TM02-02-2011

Emmanuele Ravaioli TE-MPE-TM 02-02-2011 2

Outline

The measured inductance of a main dipole at 0 current is about 80% of its nominal value. This can be observed both in the LHC during normal operation (PMBrowser data), and in the

measurement of the frequency transfer function of a dipole in SM18.

The measured magnetization is in full agreement with the theoretical magnetization calculated analytically with relations from the literature and the magnetic field calculated by

ROXIE.

In order to investigate the phenomenon, a series of dedicated tests have been carried out in SM18, featuring current cycles powered by a 4-quadrant power converter [600 A, ±10 V].

The tests showed that indeed the inductance of a main dipole can be far from its nominal value at low current (<300 A).

The cause of such a dependency is related to the magnetization effects induced within the cables of the dipole. The magnetization and its effect on the inductance can be calculated.

Interesting (and very simple) method for the measurement of the magnetization induced in a magnet: performing a current cycle, measuring V and I, and a little algebra.

LHC – Inductance of a dipole (from PM Browser!)


Calculated L of a single dipole during a typical LHC ramp

SM18 – Current cycle


MBA_1089 I = ±600 A dI/dt = ±10 A/s

SM18 – Calculated inductance


MBA_1089 I = ±600 A dI/dt = ±10 A/s

SM18 – Calculated Inductance vs Current


MBA_1089 I = ±600 A dI/dt = ±10 A/s


How to define the inductance?

Ability to store energy in a magnetic field. If magnetization is present, Ld is not equal to the nominal magnet inductance

Is it possible to calculate the magnetization M within a magnet measuring only V and I?

Magnetization

The persistent currents within the filaments of the magnet cables produce a magnetic moment.

The magnetization saturates when the filament is fully penetrated by the magnetic field.

This effect spoils the precise shape of the magnetic field.

B

J JJ

Courtesy of M. Wilson


How to calculate the magnetization using V and I?

With a little algebra one can express Ma.u. using only known parameters and measured V and I.The resulting Ma.u. is in arbitrary units and needs to be scaled with a factor Cscale.

The area of the hysteresis loop is proportional to the work done by the system, i.e. to the AC loss in the cycle.


How to scale the calculated magnetization?

How to compare the measured magnetization M with a theoretical estimation?

In a full cycle, the energy dissipated in the system must equal the energy dissipated in a hysteresis loop.The scaling factor Cscale is calculated as the value that balances the energy equality.

With a little algebra one can express M using only known parameters and measured V and I.

The resulting M is in mT and can be compared with a theoretical curve.


How to estimate the saturation curve of M?

Bx,s(I) and By,s(I) from ROXIE The components of the magnetic field of each strand of the magnet cable are calculated with ROXIE for different values of current I

The critical current density of each strand is calculated using an experimental formula

The magnetization of a strand at saturation is calculated using the Bean model

The magnetization of the whole magnet at saturation is calculated as the average magnetization in the strands weighted on the cross section of each strand

SM18 – Calculated Magnetization vs Magnetic field


MBA_1089 I = ±600 A dI/dt = ±10 A/s

11

106

7

8

9537

11 1

2

3

4

5 9

1

2

4

6

8

10

The initial magnetization (1) depends on the magnetic history of the magnet.

Before the saturation is reached, the magnetization is proportional to the applied field (1≡1a). After the saturation is reached (1b) the magnetization follows the saturation curve (1b≡2).

The two subsequent hysteresis cycles (3≡7, 7≡11) are identical.

1a1b



MBA_1089 I = ±50 A dI/dt = ±10 A/s



MBA_1089 I = ±100 A dI/dt = ±10 A/s



MBA_1089 I = ±200 A dI/dt = ±10 A/s



MBA_1089 I = ±300 A dI/dt = ±10 A/s



MBA_1089 I = ±400 A dI/dt = ±10 A/s



MBA_1089 I = ±500 A dI/dt = ±10 A/s



MBA_1089 I = ±600 A dI/dt = ±10 A/s


Summary

The measured inductance of a main dipole at 0 current is about 80% of its nominal value. This can be observed both in the LHC during normal operation (PMBrowser data), and from

the measurement of the frequency transfer function in SM18.

The measured magnetization is in full agreement with the theoretical magnetization calculated analytically with relations from the literature and the magnetic field calculated by

ROXIE.

In order to investigate the phenomenon, a series of dedicated tests have been carried out in SM18, featuring current cycles powered by a 4-quadrant power converter [600 A, ±10 V].

The tests showed that indeed the inductance of a main dipole can be far from its nominal value at low current (<300 A).

The cause of such a dependency is related to the magnetization effects induced within the cables of the dipole. The magnetization and its effect on the inductance can be calculated.

Interesting (and very simple) method for the measurement of the magnetization induced in a magnet: performing a current cycle, measuring V and I, and a little algebra.

Annex

20Emmanuele Ravaioli TE-MPE-TM 02-02-2011


Adopted symbols

V Voltage across the magnet

I Current flowing through the magnet

dI/dt Current ramp rate

Φ Magnetic flux

Ld Differential inductance

B Magnetic induction

H Magnetic field

M Magnetization

S Magnetic surface

fM Magnetic transfer function

Lnom Nominal inductance of the magnet

μ0 Vacuum permeability

Ma.u. Magnetization (arbitrary units)

Cscale Scaling factor

i Index of the i-th measurement point

c1, c2, c3, c4, c5, c6, c7, Tc0, Bc2

Bx,s Magnetic induction towards x in strand s

By,s Magnetic induction towards y in strand s

Bs Magnetic induction in strand s

T Temperature

Ic,s Critical current in strand s

Jc,SC,s Critical current density in the SC of strand s

Ms Magnetization of strand s

ASC,s Area of superconducting material in strand s

ds Diameter of a strand of the magnet cable

ns Number of strands of the magnet cable

fSC,s Fill factor (Superconductor ratio)

df Diameter of a filament of the magnet cable

Experimental parameters



MBA_1089 I = ±600 A dI/dt = ±10 A/s

SM18 – Calculated magnetization


MBA_1089 I = ±600 A dI/dt = ±10 A/s

LHC – Current ramp (from PM Browser!)


V_meas, I_meas, dI_meas/dt, L during a typical LHC ramp

Results – FTF – Dependence on the current level Gain


Configuration 2 120 A – 2 kA Without parallel resistor Low f

inductance and magnetization measurements on main dipoles in sm18 emmanuele ravaioli thanks to a....

Documents

measured magnetization

theoretical magnetization

current cycles

low current

nominal value

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naour tempe

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