Beam energy

Page maintainer: Zaven

This page is considered done. It been reviewed by Zaven. There may be missing elements, but they are all flagged and the text has no errors.

Intro

The energy of the HERA lepton beam is not constant for all years. When performing an exclusive analysis for which you need the beam energy, it is important not to use a constant value for all data taking periods. In this section the lepton beam energy measurement is discussed.

Typically the HERA electron beam energy was ~27.6GeV except in [2000] when 12GeV data was taken.

Essentials

What we usually call the beam energy is actually the beam momentum. It is stored in the field rHeraElEnergy of the table g1Beam in the uDST files. This beam momentum is computed from the electrical current through the dipoles. It is therefore based linearly on the integrated magnetic field in the arcs. These field measurements are accurate to approximately 1 per mille.

However, there is another complication. The RF frequency of the lepton accelerator is intentionally shifted. This also shifts the beam momentum away from what you would normally have computed from the dipole currents. To obtain a better estimate for the beam momentum you need to correct the value stored in the uDST files using the following relation:

${\frac {dB}{B}}={\frac {dp}{p}}={\frac {p-p_{0}}{p_{0}}}={\frac {-1}{\alpha }}\cdot {\frac {df}{f_{RF}}},$

where $p$ is the true beam momentum, $p_{0}$ is the beam momentum stored in the data files, $f_{RF}$ is the RF frequency, $df$ is the RF frequency shift, and $\alpha$ is the momentum compaction factor. In the table below the relevant parameters are summarized [1], [2]:

RF frequency offset for different data taking periods

Year	Period	RF frequency $f$ (MHz)	RF frequency offset $df$ (Hz)	$\alpha$
HERA I
1996 - 2000	Entire period	500 MHz	-150 Hz	6 10^-4
HERA II
2002	Entire period	500 MHz	Value not recorded	4.7 10^-4
2003	Until August	500 MHz	Value not recorded	4.7 10^-4
	After August	500 MHz	Detailed information available	4.7 10^-4
2004	Jan 01 - Jan 12	500 MHz	282 Hz	4.7 10^-4
	Jan 12 - Jan 19	500 MHz	252 Hz	4.7 10^-4
	Jan 19 - Aug 16	500 MHz	300 Hz	4.7 10^-4
	Shutdown - Dec 15 (13:49.00)	500 MHz	300 Hz	4.7 10^-4
	After Dec 15 (13:51.00)	500 MHz	360 Hz	4.7 10^-4
2005 - 2007	Entire year	500 MHz	360 Hz	4.7 10^-4

More info

More information can be found in this email and presentation by Zaven Akopov, who performed the scientific archeology after it was noticed that the missing energy peaks of exclusive mesons for different years did not agree.

Other beam related pages

• Beam charge
• Beam position
• Beam helicity
• Beam polarization