Chapter 4: Applications of Superconductivity

Learning Objectives

Understand major applications of superconductivity
Learn how MRI machines utilize superconducting magnets
Explore transportation applications (maglev trains)
Discover the role of superconductors in particle physics
Appreciate emerging applications in quantum computing

4.1 Medical Imaging: MRI

Magnetic Resonance Imaging (MRI) is perhaps the most successful commercial application of superconductivity. Every MRI machine contains a superconducting magnet.

Why Superconducting Magnets?

MRI requires strong, stable, uniform magnetic fields:

Requirement	Value	Why Superconducting?
Field strength	1.5 - 7 T	Normal electromagnets would need enormous power
Homogeneity	< 1 ppm	Zero resistance means no field variations from heating
Stability	Years of operation	Persistent current mode—no power supply fluctuations
Operating cost	Minimal	Only cooling costs, no Joule heating losses

MRI Magnet Specifications

Material: NbTi wire (most common)
Cooling: Liquid helium (4.2 K)
Current: ~400 A in persistent mode
Stored energy: Several megajoules
Field: 1.5 T (standard), 3 T (high resolution), 7+ T (research)

MRI Market Size

The global MRI market represents approximately 60% of all commercial superconductor applications by value. There are over 50,000 MRI scanners installed worldwide.

import numpy as np
import matplotlib.pyplot as plt

# MRI field strength vs applications
field_strengths = [0.5, 1.5, 3.0, 7.0, 11.7]
applications = ['Open MRI\n(claustrophobia)', 'Standard\nclinical',
                'High resolution\nclinical', 'Research\nimaging',
                'Ultra-high\nresearch']
market_share = [5, 60, 30, 4, 1]  # Approximate percentages

fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Bar chart: Field strength
ax1 = axes[0]
colors = plt.cm.Blues(np.linspace(0.3, 0.9, len(field_strengths)))
bars = ax1.bar(range(len(field_strengths)), field_strengths, color=colors)
ax1.set_xticks(range(len(applications)))
ax1.set_xticklabels(applications, fontsize=9)
ax1.set_ylabel('Magnetic Field (T)', fontsize=12)
ax1.set_title('MRI Scanner Field Strengths', fontsize=14)
ax1.set_ylim(0, 13)

# Add field values on bars
for bar, field in zip(bars, field_strengths):
    ax1.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.3,
            f'{field} T', ha='center', fontsize=10, fontweight='bold')

# Pie chart: Market share
ax2 = axes[1]
colors_pie = ['lightblue', 'steelblue', 'royalblue', 'navy', 'darkblue']
ax2.pie(market_share, labels=[f'{s}%' for s in market_share],
        colors=colors_pie, startangle=90, autopct='')
ax2.set_title('MRI Market Share by Field Strength', fontsize=14)

# Create legend
legend_labels = [f'{f} T - {a.replace(chr(10), " ")}' for f, a in zip(field_strengths, applications)]
ax2.legend(legend_labels, loc='center left', bbox_to_anchor=(1, 0.5), fontsize=9)

plt.tight_layout()
plt.show()

4.2 Transportation: Maglev Trains

Magnetic levitation (maglev) trains use superconducting magnets to float above the track, eliminating friction and enabling speeds over 600 km/h.

How Maglev Works

graph TB subgraph "Maglev Principle" A[Superconducting magnets
on train] --> B[Create strong
magnetic field] B --> C[Induce currents in
track coils] C --> D[Repulsive force
lifts train] D --> E[Propulsion via
linear motor] end

Operational Systems

System	Country	Speed	Technology	Status
JR-Maglev (SCMaglev)	Japan	603 km/h (record)	Superconducting	Under construction
Shanghai Maglev	China	431 km/h	Electromagnetic	Operational
Incheon Maglev	South Korea	110 km/h	Electromagnetic	Operational

SCMaglev (Japan)

Japan's superconducting maglev system uses NbTi magnets cooled by liquid helium. The Chuo Shinkansen line (Tokyo-Osaka) is under construction and will operate at 505 km/h commercially.

Levitation height: ~10 cm
Power consumption: ~1/3 of conventional high-speed rail at same speed
No wheel-rail friction or noise

import numpy as np
import matplotlib.pyplot as plt

# Speed comparison of transportation
transport = ['Car\n(highway)', 'High-speed\nrail', 'Maglev\n(Shanghai)',
             'SCMaglev\n(test)', 'Commercial\naircraft']
speeds = [120, 320, 431, 603, 900]  # km/h
colors = ['gray', 'blue', 'green', 'red', 'orange']

fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Speed comparison
ax1 = axes[0]
bars = ax1.barh(transport, speeds, color=colors, alpha=0.7)
ax1.set_xlabel('Speed (km/h)', fontsize=12)
ax1.set_title('Transportation Speed Comparison', fontsize=14)
for bar, speed in zip(bars, speeds):
    ax1.text(bar.get_width() + 10, bar.get_y() + bar.get_height()/2,
            f'{speed} km/h', va='center', fontsize=10)
ax1.set_xlim(0, 1000)

# Energy efficiency (approximate relative values)
# Lower is better - energy per passenger-km
transport_eff = ['Car\n(1 person)', 'Car\n(4 people)', 'High-speed\nrail',
                 'Maglev', 'Aircraft']
energy = [100, 25, 15, 20, 60]  # Relative values

ax2 = axes[1]
colors_eff = ['red', 'orange', 'green', 'blue', 'red']
bars = ax2.bar(transport_eff, energy, color=colors_eff, alpha=0.7)
ax2.set_ylabel('Energy (relative, per passenger-km)', fontsize=12)
ax2.set_title('Energy Efficiency Comparison', fontsize=14)
ax2.axhline(y=20, color='gray', linestyle='--', alpha=0.5)

plt.tight_layout()
plt.show()

4.3 Scientific Research: Particle Accelerators

The world's largest superconducting system is the Large Hadron Collider (LHC) at CERN, which discovered the Higgs boson in 2012.

LHC Superconducting System

1,232 dipole magnets: Each 15 m long, 8.3 T field
Material: NbTi cables
Operating temperature: 1.9 K (superfluid helium)
Total length: 27 km circumference
Stored energy: 11 GJ in magnets

Why 1.9 K Instead of 4.2 K?

At 1.9 K, helium becomes a "superfluid" with exceptional thermal conductivity. This allows better cooling of the magnets and enables higher magnetic fields (8.3 T vs. ~6 T at 4.2 K).

Other Accelerator Applications

NMR spectrometers: High-field magnets for chemical analysis
Fusion reactors (ITER): Nb₃Sn magnets for plasma confinement
Synchrotron light sources: Undulator magnets

4.4 Sensors: SQUIDs

The Superconducting Quantum Interference Device (SQUID) is the most sensitive magnetic field detector known, capable of measuring fields as small as 10⁻¹⁵ T.

How SQUIDs Work

A SQUID consists of a superconducting loop with one or two Josephson junctions. The device exploits quantum interference effects:

graph LR subgraph "SQUID Principle" A[Magnetic flux
through loop] --> B[Changes phase
of supercurrent] B --> C[Interference at
Josephson junctions] C --> D[Oscillating
voltage output] D --> E[Ultra-sensitive
flux measurement] end

SQUID Applications

Application	Field Sensitivity	Use Case
Magnetoencephalography (MEG)	10⁻¹⁴ T	Brain activity mapping
Magnetocardiography (MCG)	10⁻¹² T	Heart function monitoring
Geophysical surveys	10⁻¹¹ T	Mineral exploration
Non-destructive testing	10⁻¹⁰ T	Crack detection in metals

import numpy as np
import matplotlib.pyplot as plt

# SQUID sensitivity compared to other magnetometers
sensors = ['Hall sensor', 'Fluxgate', 'Optically pumped', 'SQUID']
sensitivity = [1e-6, 1e-10, 1e-12, 1e-15]  # Tesla

fig, ax = plt.subplots(figsize=(10, 6))

colors = plt.cm.viridis(np.linspace(0.2, 0.8, len(sensors)))
bars = ax.barh(sensors, sensitivity, color=colors, log=True)

ax.set_xlabel('Field Sensitivity (T)', fontsize=12)
ax.set_title('Magnetic Field Sensor Comparison', fontsize=14)
ax.set_xscale('log')
ax.invert_xaxis()

# Add sensitivity labels
for bar, sens in zip(bars, sensitivity):
    ax.text(sens * 0.3, bar.get_y() + bar.get_height()/2,
            f'{sens:.0e} T', va='center', fontsize=10, fontweight='bold')

# Add reference lines
ax.axvline(x=1e-12, color='red', linestyle='--', alpha=0.5)
ax.text(1e-12, 3.5, 'Brain signals\n(~10⁻¹² T)', fontsize=9, color='red', ha='center')

ax.axvline(x=5e-5, color='green', linestyle='--', alpha=0.5)
ax.text(5e-5, 3.5, "Earth's field\n(~50 μT)", fontsize=9, color='green', ha='center')

plt.grid(True, alpha=0.3, axis='x')
plt.tight_layout()
plt.show()

4.5 Power Applications

Superconducting Cables

High-temperature superconducting (HTS) cables can carry 3-5 times more current than copper cables of the same size:

No resistive losses: Zero Joule heating
Compact: Higher power density
Underground: No overhead lines needed
Current projects: AmpaCity (Germany), SuperCity (Korea)

Fault Current Limiters

Superconducting fault current limiters (SFCLs) protect power grids by instantly transitioning from superconducting to resistive state during a fault:

How SFCLs Work

Normal operation: Superconductor carries current with zero resistance
Fault occurs: Current exceeds critical value
Superconductor transitions to normal state (in milliseconds)
Resistance limits fault current, protecting equipment
System cools, superconductivity recovers automatically

4.6 Emerging Applications: Quantum Computing

Superconducting circuits are a leading platform for quantum computers, used by IBM, Google, and other major players.

Superconducting Qubits

A qubit (quantum bit) can exist in a superposition of 0 and 1 states. Superconducting qubits use Josephson junctions as non-linear elements:

Qubit Type	Description	Companies
Transmon	Charge-insensitive design	IBM, Google
Flux qubit	Uses persistent current states	D-Wave
Phase qubit	Uses phase across junction	Research labs

Why Superconducting Qubits?

Scalability: Fabricated using standard semiconductor processes
Fast gates: Nanosecond operation times
High connectivity: Can couple many qubits
Well-understood physics: Based on mature Josephson junction technology

Quantum Computing Milestones

2019: Google's 53-qubit Sycamore demonstrates "quantum supremacy"
2023: IBM's 1,121-qubit Condor processor
Future: Fault-tolerant quantum computing with error correction

import numpy as np
import matplotlib.pyplot as plt

# Quantum computer qubit count growth (approximate)
years = [2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024]
ibm_qubits = [5, 16, 20, 53, 65, 127, 433, 1121, 1121]
google_qubits = [9, 22, 72, 53, 53, 53, 53, 70, 105]

fig, ax = plt.subplots(figsize=(10, 6))

ax.semilogy(years, ibm_qubits, 'bo-', markersize=8, linewidth=2, label='IBM')
ax.semilogy(years, google_qubits, 'rs-', markersize=8, linewidth=2, label='Google')

ax.set_xlabel('Year', fontsize=12)
ax.set_ylabel('Number of Qubits (log scale)', fontsize=12)
ax.set_title('Growth of Superconducting Quantum Computers', fontsize=14)
ax.legend(fontsize=11)
ax.grid(True, alpha=0.3, which='both')

# Add annotations
ax.annotate('Google quantum\nsupremacy', xy=(2019, 53), xytext=(2017.5, 200),
           fontsize=10, arrowprops=dict(arrowstyle='->', color='red'))
ax.annotate('IBM Condor\n(1,121 qubits)', xy=(2023, 1121), xytext=(2021, 600),
           fontsize=10, arrowprops=dict(arrowstyle='->', color='blue'))

plt.tight_layout()
plt.show()

4.7 Application Overview

graph TB SC[Superconductivity] --> MED[Medical] SC --> TRANS[Transportation] SC --> SCI[Science] SC --> PWR[Power] SC --> QC[Quantum] MED --> MRI[MRI scanners] MED --> MEG[Brain imaging] TRANS --> MAG[Maglev trains] TRANS --> SHIP[Ship propulsion] SCI --> LHC[Particle accelerators] SCI --> NMR[NMR spectroscopy] SCI --> FUS[Fusion research] PWR --> CAB[Power cables] PWR --> FCL[Fault limiters] PWR --> SMES[Energy storage] QC --> QUBIT[Qubits] QC --> SENS[Quantum sensors]

Summary

Key Takeaways

MRI: Largest commercial market; uses NbTi magnets at 1.5-7 T
Maglev: SCMaglev achieves 600+ km/h using superconducting magnets
Particle physics: LHC uses 27 km of superconducting magnets at 1.9 K
SQUIDs: Most sensitive magnetic sensors (10⁻¹⁵ T)
Power systems: HTS cables and fault current limiters entering market
Quantum computing: Superconducting qubits lead the race to useful quantum computers

Practice Problems

Problem 1

An MRI magnet stores 5 MJ of energy. If this energy were released in 1 second due to a quench (sudden loss of superconductivity), what average power would be dissipated? Compare this to a typical household power consumption.

Problem 2

The SCMaglev train levitates at 10 cm above the track. If the superconducting magnets on a 300-ton train failed, how long would it take to fall to the track? (Use g = 10 m/s²)

Problem 3

A SQUID can detect magnetic fields of 10⁻¹⁵ T. Earth's magnetic field is about 5×10⁻⁵ T. By what factor is Earth's field stronger than the SQUID detection limit?