Table 3 Zonal harmonic coefficients up to the sixth order.

From: Harmonic errors of a 9.4 T all-REBCO NMR magnet affected by screening current and geometric inconsistency of coated conductors

The nth order zonal harmonic coefficients: [T/mn]

Coeff.

\(Z_0\)

\(Z_1\)

\(Z_2\)

\(Z_3\)

\(Z_4\)

\(Z_5\)

\(Z_6\)

Expo.

\(10^0\)

\(10^{-1}\)

\(10^0\)

\(10^0\)

\(10^{2}\)

\(10^{2}\)

\(10^{4}\)

Virgin

9.372

1.997

− 4.401

8.206

0.2204

8.689

2.594

Cycle1

9.387

2.003

− 3.028

8.248

0.7946

8.495

0.1853

Cycle2

9.390

2.001

− 2.721

8.263

1.063

8.452

− 0.5120

Cycle3

9.392

2.006

− 2.543

8.272

1.241

8.425

− 0.9461

Cycle4

9.393

2.006

− 2.434

8.279

1.362

8.408

− 1.226

Cycle5

9.395

2.007

− 2.326

8.285

1.483

8.391

− 1.505

Cycle6

9.396

2.007

− 2.250

8.290

1.573

8.378

− 1.706

Cycle7

9.397

2.007

− 2.188

8.295

1.651

8.398

− 1.876

Cycle8

9.397

2.007

− 2.135

8.298

1.717

8.359

− 2.018

Cycle9

9.397

2.008

− 2.081

8.301

1.782

8.349

− 2.161

Cycle10

9.398

2.008

− 2.039

8.304

1.838

8.342

− 2.279

Cycle11

9.398

2.008

− 1.999

8.306

1.889

8.334

− 2.389

Cycle12

9.398

2.008

− 1.965

8.309

1.934

8.328

− 2.485

Cycle13

9.399

2.009

− 1.931

8.311

1.979

8.321

− 2.581

Cycle14

9.399

2.009

− 1.901

8.314

2.020

8.316

− 2.666

Cycle15

9.399

2.009

− 1.894

8.314

2.032

8.315

− 2.689

Cycle16

9.400

2.009

− 1.885

8.315

2.044

8.313

− 2.716

Final

9.400

2.009

− 1.877

8.316

2.058

8.312

− 2.742