# Beam

• Each proton beam at full intensity will consist of 2808 bunches per beam.
• Each bunch will contain 1.15×1011 protons per bunch at the start of nominal fill.
• Around 30 cm. long
• With transverse dimensions of the order a mm, but in a collider as small as possible at the collision point (LHC - 16 microns fully squeezed)
• The particles in the LHC are ultra-relativistic and move at 0.999997828 times the speed of light at injection  and  0.999999991 the speed of light at top energy

### Energy in beam

• Total beam energy at top energy, nominal beam, 362 MJ

2808 bunches * 1.15 1011 protons @ 7 TeV each. = 2808*1.15*1011*7*1012*1.602*10-19 Joules = 362 MJ per beam

### British aircraft carrier

HMS Illustrious and Invincible weigh 20,000 tons all-up and fighting which is 2 x 107 kg. These are babies compared with the USS Harry S. Truman (Nimitz-class) - 88,000 tons.

Energy of nominal LHC beam = 362 MJ or 3.62 x 108 J

so 1/2 m v2 = 0.5 * 2*107 * v2 = 3.62*108
so v2 is 36.2 and v is 6.0 m/s or 11.7 knots  (or around 5.6 knots if you're an American aircraft carrier)

(1 knot = 1.852 km/hour)

### Subaru (WRX) equivalent

Kerb weight around 1800 kg

1/2 m v2 = 0.5 * 1800 * v2 = 3.62*108 gives 2280 k.p.h.

### Melting Copper

Melting point of copper: 1356 K - our magnets are at 2 K so the temperature rise needed is 1354 K

Specific heat capacity of copper: 385 Jkg-1K-1

Specific latent heat of fusion (energy required to convert a solid at its melting point into a liquid at the same temperature): 205000 Jkg-1

So to melt 1 kg of copper in the LHC we need (1354*385 + 205000) J

With one beam - 362 MJ - we can melt 362 106/(1354*385 + 205000) kg = 498.4 kg of copper

So at nominal beam current the two LHC beams together could melt nearly one tonne of copper.

### Thalys

400 tonnes - 200 m. long

0.5 * 400000 * v^2 = 3.62*10^8 therefore one beam = one 200 m. long TGV at around 150 km/h

(thanks to Jan Visser)

### TNT

The energy content of TNT is 4.68MJ/kg (Beveridge 1998).

362/4.68 = 77.4 kg of TNT

### Tevatron (proton/anti-proton)

980 GeV beam energy - 36 bunches of 2.3 e11 protons (July 2006) gives an energy per beam around 1.3 MJ

LHC > 200 times this.

The bunches are generally separated by about 7.5 m or 25 ns. (this is actually 10 RF buckets - with an RF frequency of around 400.8 MHz). However, as you guessed there are some holes in the bunch structure.

The biggest is the beam abort gap of 3 microseconds (900 m.) - this is there to give the beam dump kickers time to get up to full voltage. There are also other smaller gaps in the beam which arise from similar needs from the SPS and LHC injection kickers.

Page 2 from the following chapter in the LHC design report gives the full breakdown of the bunch structure:
https://edms.cern.ch/file/445762/3/Vol3_Chap2_v4.pdf