Beam�Current�Monitors Jean�Claude�Denard (Synchrotron�SOLEIL) DITANET�School�on�Beam�Diagnostic�Techniques 30�March�– 3�April�2009 Royal�Holloway�University�of�London�(UK)
Summary ☼ Electromagnetic field associated to�charged particle beams ☼ Destructive�monitors:�faraday�cup …. ☼ Non�destructive�monitors;�electromagnetic interaction � Wall current monitors� � Current transformers � Cavity monitors,�SQUID ☼ References DITANET�School�on� Beam�Current�Monitors 2 Beam�Diagnostics Jean�Claude�Denard
Longitudinal�E�Field�Distribution�of a�Point�Charge�in�a Conducting Tube Static charge Moving charge Ultra�relativistic charge rms length σ w =�a/√2 σ w ≈�0 σ w =�a/γ√2 a a v� =�0 v� =�ß c v� ≈ c • Moving E�field creates H�field • The Wall Current distribution�is • Charge�produces E�field inside the tube the image�of the beam • E�field induces image� • The image�charges�move along distribution but�of opposite�sign charges�of opposite�sign on� with the inner charge. and without DC�component the wall • Wall current +�beam current =�0.� Then,�Ampère’s�law,� Note:�there is no E�field ∫ (H�dl)�=�i�indicates that H�=�0� outside the tube outside the tube�(except for�DC� field). DITANET�School�on� Beam�Current�Monitors 3 Beam�Diagnostics Jean�Claude�Denard
Example of Wall Current Longitudinal�Distribution�for�a� Point!like Moving Charge Numerical Examples with a�Tube�Diam.�2a�=�50�mm kinetic energy E�for�electrons 0 100�keV 1�MeV 10�MeV for�protons 0 184�MeV 1.8�GeV 18�GeV Lorentz�factor γ 1 1.2 3 20.6 β =�(1�1/�γ 2 ) ½ 0 0.55 0.94 0.999 σ w =�a/(γ√2) 18�mm 15�mm 6�mm 0.9�mm rms length (ps)�=�a/(β γc√2) ∞ 90�ps 21�ps 2.9�ps Wall current BW�limitation�(*) 0 1.8�GHz 7.5�GHz 55�GHz (*) The actual distribution�is not gaussian,�but�for�the sake of simplicity,�its Bandwidth has� been�approximated to�that of a�gaussian distribution�of same rms length If� σ l >>a� / γ√2 ,�wall current distribution�=�beam distribution� σ l DITANET�School�on� Beam�Current�Monitors 4 Beam�Diagnostics Jean�Claude�Denard
Fields�associated�to�a�charged�particle�beam�for�a� beam�length�� σ l >>a� / γ √ 2 DITANET�School�on� Beam�Current�Monitors 5 Beam�Diagnostics Jean�Claude�Denard
Transverse�Field�Distribution Ultra�relativistic charge Moving charge Static charge v�≈ c v�=�0 v�<�c H H ρ ρ ρ E E E r r r ∫ = ( H . dl ) i ∫ = Ampère' s Law : H . dl i magnetic field no magnetic field inside → = π at� radius � r � H ( r ) i / 2 r appears � E = η TEM �wave : � � o H η = µ ε = Ω = With� � � /� � � 377 � � �vacuum � impedance o o o outside the pipe:�no E�field ε = � �vacuum � electric � permittivi ty o no magnetic field (except DC) µ = � �vacuum � magnetic � permeabili ty o DITANET�School�on� Beam�Current�Monitors 6 Beam�Diagnostics Jean�Claude�Denard
TEM�Wave in�Vacuum�Chamber is Like in�an�Air�Filled Coaxial�Transmission�Line E E H P H P i(t) i(t) ☼ Similarities :�TEM�wave carries the same EM�energy (Pointing vector P�=�E�× H):� ☼ a�monitor�can be realistically tested in�a�coaxial�line structure. ☼ Some differences : � At High frequencies (cutoff frequencies are�different in�the two cases) DITANET�School�on� Beam�Current�Monitors 7 Beam�Diagnostics Jean�Claude�Denard
Faraday�Cup Faraday�cup i Current gun Source e� ammeter ammeter • Destructive • Absolute measurement of DC�component�with an�ammeter • An�oscilloscope�or�Sample &�Hold measures the peak current in� case�of pulsed beam . • Can�be used for�the calibration�of non�destructive�monitors�that provide relative�measurements.�For�example FC�calibrates an�RF� cavity current monitor�on�CEBAF�injector (CW�superconducting Linac). DITANET�School�on� Beam�Current�Monitors 8 Beam�Diagnostics Jean�Claude�Denard
Faraday�Cup;�Design�Issues ☼ Absolute accuracy is usually around 1%,�it is difficult to�reach 0.1%. ☼ Needs to�absorb all the beam:�block�with large�entrance�size and thickness >>� radiation�length.�A�FC�built at DESY�and presently used on�a�low current 6� GeV beam at JLAb uses�1�m 3 of lead (12�tons). ☼ Backscattered particles (mostly e � ):�narrow entrance�channel,�bias voltage�or� magnetic field redirect the backscattered e � on�the FC.�Accuracy evaluation requires Monte�Carlo�simulations�(EGGS�from SLAC;�GEANT�from CERN). ☼ Power (W)�=�E�in�MeV × I�in�]A.� Example:�5�MeV FC�in�CEBAF�injector�with�200�]A�CW�beam�→ 1000�W.� A�cooling�circuit�takes�the�power�out.�The�isolation�is�done�with�de�ionized� water�and�insulating�rubber�tubes.� ☼ Safety�issues:�FC�needs�to�be�always�terminated�by�a�DC�circuit�to�avoid� arcing�and�a�potentially�dangerous�high�voltage�that�would�develop�at�cable� end.�A�pair�of��high�impedance�diodes�can�be�connected�in�parallel�on�the�FC� output.� DITANET�School�on� Beam�Current�Monitors 9 Beam�Diagnostics Jean�Claude�Denard
SLS�Wide Bandwidth Coaxial�Faraday�Cup (0!4�GHz) 50�ohm Coaxial structure beam M.�Dach�et�al.�(SLS)�;� BIW2000 DITANET�School�on� Beam�Current�Monitors 10 Beam�Diagnostics Jean�Claude�Denard
Calorimeter ☼ Calorimetry refers to�a�direct�measurement of the total�energy delivered to�a� massive�block�of metal (silver or�tungsten)�over a�period of time. ☼ Total�energy is determined by�measuring the temperature rise of the object if: � The average beam energy is precisely known � Any energy losses can be accounted for�by�reliable calculation or�direct� measurement. ☼ A�calorimeter has�been�developed for�CEBAF�CW�beam (A.�Freyberger,�to� be published) DITANET�School�on� Beam�Current�Monitors 11 Beam�Diagnostics Jean�Claude�Denard
Wall Current Monitor:� Beam and Wall Current Spectra for�Ultra�Relativistic Beams Time�domain Frequency�domain ↓ DC 1/T τ ←i�beam→ τ t f 1/2 πτ πτ πτ πτ 0 T T ←i�wall→ t f 0 No�DC DITANET�School�on� Beam�Current�Monitors 12 Beam�Diagnostics Jean�Claude�Denard
Wall Current Monitor:�Concept v out v out t r i wall v out i beam r i wall v out =�i wall *�r DITANET�School�on� Beam�Current�Monitors 13 Beam�Diagnostics Jean�Claude�Denard
WCM:�From�Concept�to�Actual�Implementation C gap ] ☼ For�vacuum�quality:�ceramic gap� ☼ r�is made of several resistors in� i wall parallel,�distributed around the gap.� Special chip�resistors still behave r as�resistors in�the GHz�frequency i wall ] range. L ☼ Electrical shield:�avoids parasitic external currents flowing through r,� WCM�response and prevents the beam EM�field log�amplitude from radiating outside the monitor.� ☼ High ]�material fills the space ω (log scale ) between gap�and shielding for�low ω = π r L 1 rC 2 f gap frequency response. ; ; = L o r h Ln ( b / a ) π 2 DITANET�School�on� Beam�Current�Monitors 14 Beam�Diagnostics Jean�Claude�Denard
Implementation Example:�6�kHz�to�6�GHz�WCM�:�(R.� Weber�BIW93) Ceramic gap�and surface�mounted resistors ferrites ferrites Resistors are�not pure�resistors at high frequencies ≈ 6�nH Resistor with 5�mm�wire connections ≡ r r ≈ 1�pF In�the GHz�range,�standard�resistors are�replaced by�Surface�Mounted Resistors that have�smaller inductance�and capacitance.� DITANET�School�on� Beam�Current�Monitors 15 Beam�Diagnostics Jean�Claude�Denard
6�kHz�to�6�GHz�WCM�:�(R.�Weber) ☼ r�=�1.4�ohm�(80�resistors in�parallel). ☼ rC gap circuit�at high frequencies � Ceramic gap�considered as�a�lump� t�(thickness) capacitor:� w S d m =�90�mm;� t =�3.2�mm;�and w =�4.5mm� = ε ε C =>�� C gap =�33�pF gap 0 r d m t 1 = = and � f 3 . 4 GHz π 2 rC h ≅ π S w * 2 d gap m � Ceramic gap�behaves as�a�radial� ε ≈ alumina : � 9 . 5 transmission�line matched to�its 1.4a r characteristic impedance:� f h >�6�GHz� (measured) h Shield =�1�turn ☼ rL circuit�at low frequencies a r = = = b f low 5 . 6 � kHz �with L 40 ]H ; ; π 2 L = L o r h Ln ( b / a ) π 2 DITANET�School�on� Beam�Current�Monitors 16 Beam�Diagnostics Jean�Claude�Denard
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