Inductance and magnetization measurements on main dipoles in SM18 Emmanuele Ravaioli Thanks to A. Verweij, S. Le Naour TE-MPE-TM

Emmanuele Ravaioli TE-MPE-TM 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!) Emmanuele Ravaioli TE-MPE-TM Calculated L of a single dipole during a typical LHC ramp

SM18 – Current cycle Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±600 AdI/dt = ±10 A/s

SM18 – Calculated inductance Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±600 AdI/dt = ±10 A/s

SM18 – Calculated Inductance vs Current Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±600 AdI/dt = ±10 A/s

Emmanuele Ravaioli TE-MPE-TM How to define the inductance? Ability to store energy in a magnetic field. If magnetization is present, L d 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 J J Courtesy of M. Wilson

Emmanuele Ravaioli TE-MPE-TM How to calculate the magnetization using V and I? With a little algebra one can express M a.u. using only known parameters and measured V and I. The resulting M a.u. is in arbitrary units and needs to be scaled with a factor C scale. The area of the hysteresis loop is proportional to the work done by the system, i.e. to the AC loss in the cycle.

Emmanuele Ravaioli TE-MPE-TM 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 C scale 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.

Emmanuele Ravaioli TE-MPE-TM How to estimate the saturation curve of M? B x,s (I) and B y,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 Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±600 AdI/dt = ±10 A/s 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. 1a 1b

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±50 AdI/dt = ±10 A/s

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±100 AdI/dt = ±10 A/s

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±200 AdI/dt = ±10 A/s

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±300 AdI/dt = ±10 A/s

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±400 AdI/dt = ±10 A/s

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±500 AdI/dt = ±10 A/s

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±600 AdI/dt = ±10 A/s

Emmanuele Ravaioli TE-MPE-TM 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 20 Emmanuele Ravaioli TE-MPE-TM

21 Adopted symbols VVoltage across the magnet ICurrent flowing through the magnet dI/dtCurrent ramp rate ΦMagnetic flux L d Differential inductance BMagnetic induction HMagnetic field MMagnetization SMagnetic surface f M Magnetic transfer function L nom Nominal inductance of the magnet μ 0 Vacuum permeability M a.u. Magnetization (arbitrary units) C scale Scaling factor iIndex of the i-th measurement point c 1, c 2, c 3, c 4, c 5, c 6, c 7, T c0, B c2 B x,s Magnetic induction towards x in strand s B y,s Magnetic induction towards y in strand s B s Magnetic induction in strand s TTemperature I c,s Critical current in strand s J c,SC,s Critical current density in the SC of strand s M s Magnetization of strand s A SC,s Area of superconducting material in strand s d s Diameter of a strand of the magnet cable n s Number of strands of the magnet cable f SC,s Fill factor (Superconductor ratio) d f Diameter of a filament of the magnet cable Experimental parameters

SM18 – Calculated Magnetization vs Magnetic field Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±600 AdI/dt = ±10 A/s

SM18 – Calculated magnetization Emmanuele Ravaioli TE-MPE-TM MBA_1089I = ±600 AdI/dt = ±10 A/s

LHC – Current ramp (from PM Browser!) Emmanuele Ravaioli TE-MPE-TM V_meas, I_meas, dI_meas/dt, L during a typical LHC ramp

Results – FTF – Dependence on the current levelG ain Emmanuele Ravaioli TE-MPE-TM Configuration 2120 A – 2 kAWithout parallel resistorLow f