PSFC/JA-18-55

Design of a Tabletop Liquid-Helium-Free 23.5-T Magnet Prototype Toward 1-GHz Microcoil NMR

Dongkeun Park, Yoon Hyuck Choi, Yukikazu Iwasa

October 2018

Plasma Science and Fusion Center Massachusetts Institute of Technology

Cambridge MA 02139 USA

This work was supported by the National Institute of General Medical Sciences of the National Institutes of Health under award R21GM129688. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

Submitted to IEEE Transactions on Applied Superconductivity

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Design of a Tabletop Liquid-Helium-Free 23.5-T Magnet Prototype towards 1-GHz Microcoil NMR

Dongkeun Park, Yoon Hyuck Choi, and Yukikazu Iwasa

Abstract— We present a design study of a liquid-helium (LHe)-free 23.5-T, ϕ25-mm RT-bore REBCO magnet for high-

resolution 1-GHz microcoil nuclear magnetic resonance (NMR) spectroscopy. A microcoil NMR magnet is compact and thus its cost will be less by nearly an order of magnitude than that of the

standard NMR magnet, and placeable on a bench, thereby result-ing in a large saving in space. In addition, LHe-free operation en-ables the user to be independent from a cooling source in short

supply. This paper includes: 1) magnet design and conductor re-quirement specification; 2) conceptual design of a full-scale tab-letop LHe-free 1-GHz NMR magnet; and 3) design of a 10-K op-

erating REBCO 23.5-T magnet prototype with a ϕ20-mm cold-bore. This small-size magnet prototype will be built and tested by 2020 for validation of performance and manufacturing challeng-

es such as splices between coils. The paper concludes with discus-sion of stray-field shielding methods and a screening-current-inducing field (SCF) effect.

Index Terms—High-field magnet, Liquid-helium-free, Micro-

coil NMR, REBCO, Tabletop.

I. INTRODUCTION

NE of the primary goals for technical development in nu-

clear magnetic resonance (NMR) spectroscopy is to in-

crease the sensitivity, defined as the signal-to-noise ratio, and

the resolution of NMR instrumentation. In microcoil NMR

probes for which a sample size is <10 µL and the diameter of

a radio-frequency (RF) coil is <1 mm, the mass sensitivity is

much higher (10-100 times) than in conventional 5-mm

Helmholtz coil NMR probes due to its feasibility of strong RF

irradiation [1]-[3]. A compact microcoil NMR spectroscopy

with a smaller room temperature (RT) bore than conventional

ones has merits in cost and installation siting too.

A higher-field magnet offers better peak resolution and sen-

sitivity, both increased with the magnetic field to the power of

1.5, enabling analysis of larger molecules like complex pro-

teins. Currently available or being developed ≥1-GHz NMR

magnets are very expensive and require a vast installation site

to keep 5-gauss line of at least >40 m2 even with an actively

shielded magnet [4], limiting ≥1 GHz NMR spectroscopy to a

few labs in the world. Therefore, we believe that a market de-

mand for affordable, small-footprint and high-field magnets

Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under award number R21GM129688. (Corresponding author: Dongkeun Park)

D. Park, Y. H. Choi and Y. Iwasa are with the Francis Bitter Magnet Labora-tory / Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (e-mail: dk_park@mit.edu).

for microcoil NMR spectroscopies will grow significantly.

Liquid helium (LHe) has been used to cool and operate all

conventional high-field superconducting NMR magnets, but as

the price has quadrupled in the last decade by global helium

shortage [5], [6], to develop cooling options that do not rely on

LHe has become more urgent and imperative than ever.

At the Magnet Technology Division of the MIT Francis Bit-

ter Magnet Laboratory, we have proposed a tabletop LHe-free

23.5-T high-temperature superconductor (HTS) magnet for 1-

GHz microcoil NMR spectroscopy (Micro-1G). In this paper,

we describe first the magnet design required specifications

with conductor performance requirements, secondly a concep-

tual design of a tabletop magnet for Micro-1G, and thirdly de-

sign of a 10-K REBCO 23.5-T/ϕ20-mm-cold-bore magnet to

be built for validation tests. Finally, we conclude with discus-

sion about stray-field shielding methods, and a screening-

current-inducing field (SCF) with its mitigating schemes.

II. CONCEPTUAL DESIGN OF MICRO-1G

A. Design Requirement Specifications

Key design specifications of the superconducting magnet

for Micro-1G are: 1) 23.5-T center field with a ϕ25-mm RT

bore; 2) field homogeneity of <0.01 ppm over 5-mm DSV; 3)

5-gauss fringe field radius of <1 m; and 4) LHe-free operation

at 10 K. We will adopt three techniques—superconducting,

ferromagnetic, and RT shimming—to compensate field errors

and thus to achieve required homogeneity. The ϕ25-mm RT

bore specification has consequence for the positions of coil

winding diameter of 58 mm by considering radial spaces for

cryogenic components, vacuum, and HTS shims coils.

Of the commercially available superconductors, REBCO

conductor is the most practically suitable conductor for Micro-

1G magnet because of its high field performance, high hoop

strength, and no heat treatment required. We have chosen 6-

mm and 8-mm wide, 65-μm thick REBCO conductor with sur-

round 5-μm electroplated copper layer on each side. The re-

quired minimum critical current, Ic, and hoop stress would be

470 A·cm-1-w (at Top=10 K, B∥ c=10 T) and 600 MPa (at

Ic/Ic0=0.95 under stress), respectively, for conceptual design of

Micro-1G magnet based on a standard 7.5% Zr pinning REB-

CO conductor manufactured by SuperPower Inc. [7].

O

2

B. First-Cut Design of a Micro-1G Magnet

Table I shows a first-cut design of a 23.5-T magnet for Mi-

cro-1G operating at 10 K. We adopt a no-insulation (NI) wind-

ing technique with REBCO conductor enabling the magnet to

be compact, robust, and self-protecting. A simple single sole-

noid coil formation can result in a more affordable, high-field

NMR magnet occupying a smaller footprint. An 8-mm wide

REBCO conductor is used for C4 coils for its increased Ic, al-

lowing the magnet to operate at 225 A and ≥10 K with margin.

The computed maximum hoop stress is 450 MPa considering

energization only and assuming isotropic solid-body winding.

In high-field magnets, stresses are one of the most important

design constraints, thus, more detailed analysis and validation

are necessary. A double-notched winding structure enhances a

spatial field homogeneity. Computed peak-to-peak homogene-

ity in 5-mm DSV is 0.6 ppm and the 2nd order (Z2) harmonic

terms of -5,926 Hz·cm-2 is a dominant error from the as-

designed magnet analysis. However, as-built magnet will be a

few orders away from its designed homogeneity due to the

field errors caused by electromagnetic force contrac-

tion/expansion, material tolerance, manufacturing errors, SCF

and any other uncertainties, and the errors will be compen-

sated by shimming. A 5-gauss fringe field radius of 2 m is be-

yond the design requirement of 1 m, thus the design needs to

be refined to have an iron yoke shield or active shield coils af-

ter more investigation.

Toward a detailed engineering design of a tabletop LHe-

free Micro-1G magnet from its first-cut design, we have pro-

posed and started to develop a small-scale 23.5-T REBCO

magnet prototype operated at ≥10 K for validation tests in a 2-

year program sponsored by National Institutes of Health,

United States.

III. CRYOGEN-FREE 23.5-T PROTOTYPE MAGNET

A. Coil Design

With the prototype, we expect to validate or investigate: 1)

conductor performance; 2) NI coil characteristics; 3) conduc-

tion-cooled cryogenic system; 4) manufacturing technique; 5)

thermal dynamics during charging, operating, and quench; 6)

SCF reduction methods; and 7) fringe field shielding methods.

Fig. 1 illustrates a proposed prototype magnet: (a) a to-scale

cross-section drawing; and (b) a circuit model including NI

turn-to-turn resistance, RC. The magnet is a stack of REBCO

NI pancake coils. Two 25-µm thick Kapton films are used as

an insulated spacer between all pancake coils, and 0.2-mm

TABLE I

FIRST-CUT DESIGN OF 23.5-T REBCO MAGNET FOR MICRO-1G

Parameters C1 C2* C3* C4*

Conductor Width /

Thickness [mm]

6 /

0.065

6 /

0.065

6 /

0.065

8 /

0.065

Spacer Thickness [mm] 0.26 0.26 0.26 0.26

Winding Inner (ID) /

Outer Diameter (OD) [mm]

60.73 /

132.75

59.56 /

132.75

58.00 /

132.75

58.00 /

132.75

Lower /

Upper Extent [mm]

-25.04 /

25.04

25.04 /

37.56

37.56 /

112.68

112.68 /

128.94

Number of DPs /

Turns per DP

4 /

1108

2x 1 /

1126

2x 6 /

1150

2x 1 /

1150

Length per DP [m] 337 340 345 345

Total Length [km] 6.86

Total Inductance [H] 12.15

Operating current, Iop [A] 225

Center Field @ Iop [T] 23.5

Homogeneity [ppm] 0.6 @ 5-mm DSV

5 Gauss Radius [m] (Axial) 2.5, (Radial) 2.0

* Mid-plane symmetry

h= 7

7.4

mm

2a2=104.5 mm

8-mm wide

REBCO

2a1= 20 mm

6-mm wide

REBCO

Insulation (+ Cooling Channel)

between (Double) Pancake Coils

C1

C2

C3C4C5C6

C12

C7C8C9C10C11

(a)

RC2-1

LC2-1

RC1-1

LC1-1

RC2-10

LC1-10

RC2-2

LC2-2

DC

L1 L2 L11 L12

RC 1 RC 2 RC 11 RC 12

RS 12RS 11RS 2RS 1

icoil 1 icoil 2 icoil 12icoil 11

iPS

iRc1 iRc2 iRc11 iRc12

M1,2 … M2,11 … M11,12

Vd

(b)

Fig. 1. A 23.5-T magnet prototype: (a) cross-section view; (b) circuit model

for charging/discharging and quench analysis.

TABLE II

KEY DESIGN PARAMETER OF 23.5-T REBCO MAGNET PROTOTYPE

Parameters C2 – C11 C1, C12

Conductor Width [mm] 6 8

Conductor Thickness [mm] 0.065

Insulated Spacer Thickness [mm] 0.05 or 0.25

Winding ID / OD (2a1 / 2a2) [mm] 20 / 104.5

Lower Extent (b1) [mm] -30.65 -38.9 / 30.9

Upper Extent (b2) [mm] 30.65 -30.9 / 38.9

Number of Pancakes 10 2 × 1

Turns per Pancake 650

Conductor Length (Pancake / Total) [m] 128 / 1,536

Total Inductance [H] 1.38

Operating Current (Iop) [A] 231.5

Operating Temperature (Top) [K] <10

Center Field @ Iop [T] 23.5

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thick copper sheets are inserted between two Kapton films in

every two spacers. Table II lists key parameters of the proto-

type magnet. With a winding inner diameter of 20 mm, we use

a total conductor length of 1.54 km to achieve the center field

of 23.5 T corresponding to a proton resonant frequency of 1

GHz, same as Micro-1G. As in the first-cut design of Micro-

1G magnet, an 8-mm wide REBCO conductor is used for end

pancake coils (C1 and C12) to have enough Ic margin at ≥10

K. The estimated charging delay time constant is about 75 s

assuming the average turn-to-turn resistivity is 50 µΩ·cm2 [7].

B. Stresses and Strains

The stress calculation has been carried out based on elastic

continuum mechanics with a force equilibrium equation. We

plan to build the REBCO magnet with dry-winding, i.e. no

epoxy bonding between turns, to avoid delamination issue [8].

A thick radial build dry magnet like our prototype (a1/a2>5)

can no longer be assumed as a solid body winding model be-

cause it is not physically possible to have a tensile radial stress

between turns but they try to be separated instead. Thus, we

use a finite element method with a pancake model having all

turns. Radial and hoop stresses are built up in the coil during

winding, cooling-down, and energization. Fig. 2 shows calcu-

lation results for both radial and hoop stresses of the prototype

magnet. The winding tension is an important parameter to de-

termine final peak stresses in the magnet. With a 20-N wind-

ing tension, a radial stress in the inner 10-mm winding section

becomes almost zero which means no contact between turns.

A compressive (negative) radial pressure is preferable to have

good thermal contacts in this cryogen-free prototype magnet

and to keep the current bypass feature in NI winding for self-

protection against thermal runaway. We expect to keep com-

pressive radial pressure with increasing winding tension to

50 N and it also suppresses hoop stress below 150 MPa which

is far below the conductor’s stress limit of ~700 MPa [9]. A

winding with REBCO side facing inward, i.e. negative bend-

ing strain, may also be of help to secure more stress margin.

This sufficient stress margin allows for the prototype magnet

to be safely subjected to over-current in current-sweep-

reversal testing to be discussed later in this paper.

C. Stability and Multi-Coil Quench Analysis

An HTS magnet typically has a stability margin at least 100

times greater than that of low-temperature superconductor

(LTS), i.e. HTS magnets are not susceptible to quench caused

by disturbances that affect LTS magnets [10]. Because of a

single coil formation which has no interaction force from out-

side, this prototype magnet should be self-protecting in any

realistic quench situation. The quench behavior is simulated

using a lumped parameter model developed for NI coils as

shown in Fig. 1(b) assuming a sudden quench initiated from a

top pancake coil (C1), one of the worst scenario. The govern-

ing equation of the circuit model to calculate coil current, icoil,

can be expressed as:

0

coilPSCcoilS

coilM iiRiR

dt

diL (1)

and the power supply current, iPS, bypassed through a diode

during quench also can be expressed as:

121

121211

CC

dCCPS

RR

VRiRii

(2)

and each coil temperature, Tcoil, can be calculated from:

TcoilScoilPSCcoilcoil

p qjjjTkt

TC

22 (3)

where (LM) is the magnet inductance matrix, (RC) and (ρC) rep-

resent turn-to-turn resistance and resistivity, and (RS) and (ρS)

represent copper matrix resistance and resistivity which appear

if the coil temperature exceeds current sharing temperature,

TCS, or the coil current exceeds Ic for each pancake coil, and Vd

is a diode voltage. Cp is the effective specific heat for each

pancake coil, k is the effective thermal conductivity between

pancake coils, jps and jcoil are the power supply current density

and coil current density, and qT is the arbitrary power density

applied to a pancake coil (C1) only for triggering quench.

Simulated results are shown in Fig. 3. Due to large Ic mar-

gin, thus high TCS, in middle section pancake coils, the in-

duced current caused by magnetic coupling in C7 soars up to

Fig. 2. Hoop stress and radial distributions in the midplane pancake coil

(C6) along radius with the cases of 20-N and 50-N winding tension (WT).

(a) (b)

Fig. 3. Results of the magnet quench initiated from C1 by using a lumped

equivalent circuit model analysis: (a) azimuthal direction coil current, iCoil; and

(b) temperature of coils, Tcoil.

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890 A. The peak hoop stress derived from this current can be

750 MPa, almost marginal stress level. Maximum coil temper-

ature will not exceed more than 100 K.

D. Thermal Analysis and Conduction-Cooled System

Fig. 4(a) shows a half-section view of a NI pancake coil

model used for thermal analysis during charging at 0.1 A·s-1.

Heat transfer in the model is dominated by thermal contact re-

sistances between copper, Kapton, and an upper surface of NI

pancake winding. Average charging loss per pancake coil

from (1), Pcoil= (iPS – icoil)2·Rc, is 80 mW. Estimated joint dis-

sipation per pancake coil is <2 mW at Iop=231.5 A.

With axial pressures of 18–52 MPa exerted on the interfaces

between spacers and pancake coils by electromagnetic force,

thermal contact conductance can be >10 W·m-2·K-1, very con-

servatively low number compared with the value in [11]. We

assumed the temperature of outer ends of copper spacers are

constant 10 K. Computed peak temperature in the half sym-

metric magnet model is <13 K as shown in Fig. 4(b), and

based on estimated temperature margin of >20 K, the proto-

type magnet should be thermally stable during charging.

Fig. 5 shows a to-scale, partial section view of the conduc-

tion-cooled cryogenic system. The prototype magnet will be

suspended from the copper disk block directly anchored to the

2nd stage coldhead of a two-stage cryocooler (2nd-stage

block) with a cooling capacity of 8 W at 10 K, sufficient to

keep the prototype magnet system at 10 K. Thermal radiation

from room temperature outside a cryostat is intercepted by a

copper radiation shield attached to the 60-W@50-K 1st stage

coldhead. Copper spacers between every two pancake coils are

thermally linked to a cooling bar fixed to the 2nd-stage block.

HTS leads will also be anchored to the 2nd-stage block. For

≥10 K testing, the heater embedded in the 2nd-stage block

may need to be powered. For a Micro-1G, mechanical vibra-

tions from cryogenic system must be suppressed by using a

low vibration pulse-tube cryocooler and/or adopting a vibra-

tion isolating system. In this prototype magnet, however, we

do not consider any vibration issue.

IV. DISCUSSION

A. Stray Field Shielding Methods

A Micro-1G requires a small 5-gauss fringe field radius to

minimize siting area. Unlike the conventional LTS magnets

employing active shielding coils because of its lightweight and

compactness, REBCO conductor is tens of times more expen-

sive than LTS NbTi wire, so a passive shielding with using

ferromagnetic yoke seems more viable for Micro-1G. Sur-

rounding ferromagnetic yoke expects to not only limit 5-gauss

fringe field but also shield external interference. Because it af-

fects the center field, main coil design needs to be refined. We

will first investigate the nonlinear magnetic properties of the

ferromagnetic materials at 10 K, and then, select a shielding

material most suitable for Micro-1G. We will validate it by

testing with the 23.5-T magnet prototype.

B. SCF Mitigating Schemes

One prominent field error source in HTS magnets is SCF

[12], [13]. Because SCF is proportional to radial field, perpen-

dicular to the tape surface and largest in the both end DP coils,

and Ic, which is not uniform along the stacked DPs, the SCF

generates strong first and second order harmonic errors which

may not be small enough to be compensated by shimming.

SCF will be reduced as the operating condition and super-

conductor’s critical conditions are getting close. Two SCF-

reduction methods will be investigated and validated using the

23.5-T magnet prototype: 1) Temperature control by bifilar

disk heaters next to top/bottom end pancakes to increase Top

close to TC [14]; and 2) Current sweep reversal to increase Iop

close to operation margin [15].

V. CONCLUSION

We have introduced a compact, high-performance microcoil

NMR magnet, and presented design of a small-scale 23.5-T

REBCO magnet prototype to be built and tested for validation

by 2020. We believe that successful completion of validation

for key features of the prototype will pave a way to a full-scale

affordable tabletop LHe-free 1-GHz magnet for high-

resolution microcoil NMR spectroscopy. The enabling fea-

tures validated by the prototype will become viable for the

next generation ≥1-GHz NMR, thereby enabling new and

high-impact applications of superconductivity to biomedical

research.

[K]

(a) (b)

Fig. 4. Thermal analysis of the prototype magnet: (a) an NI pancake model;

and (b) temperature during ramp up with 0.1 A·s-1 of a half magnet model.

Fig. 5. To-scale view of conduction-cooled cryogenic system.

5

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