# Kinetic energy of relativistic electrons

1. Jul 26, 2009

### neptunone

Gentleman,

My questions are the following:

1.) If It takes 534 kJ to remove one mole of electrons from the atoms at the surface of a solid barium aluminate metal, how many kJ would it take to generate one gramm of electrons ?

2.) How much kinetic energy do one mole of electrons accelerated to relativistic speed (.9 c) have ?

3.) How much energy is required for the LINAC(1.1) to accelerate said mole of electrons to .9 c ?

Additional Info:

The LINAC consists of five Klystrons with the following characteristics:

C Band frequency Klystron E3783 –
Operating Frequency 2856 MHz
Peak Output Power 4.5 MW
Average Power 2.8 MW
Power efficiency 44 %
Gain (dB) 48 %
Pulse Length Duration 20 usec typical
Pulse Repetition 250 pps
Gun Voltage 130 KV
Beam Current 85 amps

Thank you for your help.

Sincerely

neptunone

2. Jul 26, 2009

### tiny-tim

Welcome to PF!

Hi neptunone! Welcome to PF!

(oh, and it's "Gentlemen" )

Show us what you've tried, and where you're stuck, and then we'll know how to help!

3. Jul 26, 2009

### Bob S

Using a work function of 1 eV per electron to pull it out of the cathode, it will take 96,300 joules to pull a mole of electrons out. So your barium titenate cathode must have a work function of 5.5 eV. The proton's mass is about 1 gram per mole, and the electron's mass is 1836 times less, so 1 gram of electrons is 1836 moles. 0.9 c equals a gamma of 2.29, so the total mass is 2.29 times as high, kinetic energy 1.29 times.
Is your 85 amps is the klystron beam current, and not the electron beam current? 2856 MHz is not very good for high electron beam current. (I used to work on a 2856 MHz Varian-built linac).

4. Jul 27, 2009

### neptunone

Dear tiny-tim, dear Gentlemen

Please forgive me for the typo. I would like to thank Bob S for his reply. That was very helpful.

0.9 c equals 2.29 gamma, the kinetic energy 1.29, so far so good.

That leaves the last question: How much energy is required for the LINAC (5 x 45 GeV, 4.5 MW each) to accelerate said mole of electrons to .9 c ?

Thank you very much for your time and patience.

Sincerely yours

neptunone

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