Kern- und Teilchenphysik SS2012

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KIT – Universität des Landes Baden-Württemberg und

nationales Forschungszentrum in der Helmholtz-Gemeinschaft

KIT-Centrum Elementarteilchen- und Astroteilchenphysik KCETA

www.kit.edu

KIT – Universität des Landes Baden-Württemberg und

nationales Forschungszentrum in der Helmholtz-Gemeinschaft

KIT-Centrum Elementarteilchen- und Astroteilchenphysik KCETA

www.kit.edu

Kern- und Teilchenphysik SS2012

Johannes Blümer

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Themen und Inhalte der Vorlesung

1) Di 17. April Übersicht, Notation, Kinematik

Inhaltsverzeichnis, Übungsbetrieb, Literatur, Notationen, Tour de Force, relativistische Kinematik 2) Do 19. April Beschleuniger

HV-Erzeugung, stat. Generatoren, Linearbeschleuniger, zykl. Beschleuniger, Kollider, kosm. Beschleuniger 3) Di 24. April Detektoren 1

Wechselwirkung von Teilchen und Strahlen mit Materie; experimentelle Methoden 4) Do 26. April Detektoren 2

Detektorbaukasten; Grossdetektoren; andere Anwendungen - Di 1. Mai Tag der Arbeit

5) Do 3. Mai Atomkerne 1

Streuversuche, Entdeckung der Atomkerne, Rutherford; Eigenschaften stabiler Kerne 6) Di 8. Mai Atomkerne 2

Masse, Bindungsenergie, Form von Kernen; Kernkräfte und Kernmodelle 7) Do 10. Mai Kernreaktionen 1

Spontane Zerfälle (Alpha, Beta, Gamma-Zerfälle);

8) Di 15. Mai Kernreaktionen 2

induzierte Kernspaltung, Kerntechnik; Kernfusion - Do 17. Mai Himmelfahrt

9) Di 22. Mai Kernphysik im Universum

Elementsynthese im Urknall; ~ in Sternen, Sternentwicklung, Supernovae; Kosm. Strahlung 10) Do 24. Mai Nukleonen 1

Elastische Streuung, Formfaktoren, Ladungsradien 11) Di 29. Mai Nukleonen 2

Tiefinelastische Streuung, angeregte Zustände von Nukleonen, Strukturfunktionen, Partonen, Quarks 12) Do 31. Mai Quarks, Gluonen, Hadronen

Quarkstruktur der Nukleonen, Quarks in Hadronen, qg-WW, Skalenverhalten 13) Di 5. Juni e+e- Kollisionen

Teilchenproduktion, Leptonpaare, Resonanzen, nicht-resonante Hadronproduktion, Gluonen - Do 7. Juni Fronleichnam

14) Di 12. Juni Symmetrien und Erhaltungssätze

Kontinuierliche und diskrete Symmetrien; C, P, CP, CPT 15) Do 14. Juni Schwache Wechselwirkung

Neutronen, Betazerfall, Paritätsverletzung, V-A-Wechselwirkung 16) Di 19. Juni Neutrale Kaonen

Kaonen, CP-Verletzung, CKM-Matrix 17) Do 21. Juni Neutrinos als Sonde

Geladene und neutrale Ströme, Neutrino-Quark-Streuung 18) Di 26. Juni W und Z Bosonen

Entdeckung und Eigenschaften, Bedeutung der Präzisionsmessungen 19) Do 28. Juni Das Standardmodell

20) Di 3. Juli Neutrino-Oszillationen

Neutrinos aus der Sonne, aus Beschleunigern und Reaktoren 21) Do 5. Juli Neutrinomasse

Neutrinomasse im Standardmodell, kosmologische Bedeutung; Betazerfall (KATRIN etc.), 0νββ-Zerfall 22) Di 10. Juli Dunkle Materie

Evidenzen für DM; Teilchenkandidaten; Entdeckungsversuche 23) Do 12. Juli Kosmische Strahlung

Beschleunigung, Ausbreitung in der Galaxie, Luftschauer, extragal. K.S., Bedeutung für Astro- und Teilchenphysik 24) Di 17. Juli Astroteilchenphysik

Die Querverbindungen zwischen Astronomie, Kosmologie, Kern- und Teilchenphysik v. Urknall bis zum Higgs 25) Do 19. Juli Offene Fragen, neue Projekte

Aktuelle und geplante Experimente/Messungen

IKP in KCETA KT2012 Johannes Blümer

Inhalt

2

http://www.auger.de/~rulrich/lehre/kerneteilchen2012/index.html

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KT2012 Johannes Blümer IKP in KCETA

Betatron

3

R.M. Jones, Physics of Particle Accelerators, PHYS 4722, Circular Accelerators Lecture, 2011.

2

2 1 2 1 1

2 B p

qr

p E d

B r,t

qr r r dt

B r,t B dS

r

19 19

1. Particles accelerated by the rotational electric field generated by a time varying magnetic field.

2. In order that particles circulate at constant radius: ^dt E d

r

S d dt B

l d d E

t E B

2 B-field on orbit is one half of the average B over the circle. This

imposes a limit on the energy that can be achieved. Nevertheless the

constant radius principle is attractive for high energy circular accelerators.

Oscillations

about the design orbit are called betatron

oscillations

Magnetic flux,

Generated E-field

r

Betatron

Kerst and Serber built the first Betatron (1941)

Jones

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KT2012 Johannes Blümer IKP in KCETA 4

R.M. Jones, Physics of Particle Accelerators, PHYS 4722, Circular Accelerators Lecture, 2011.

20

Betatron Motion

Exercise 2: As the oscillations from the design orbit in almost any accelerator are referred in terms of “betatron”

motion it is clearly important to understand this phenomena. Unsuprisingly, it was originally ascribed to oscillation in a betatron, but the name stuck!

In cylindrical coordinates the equation of motion for electrons is:

Where r and z refer to radial outward and vertical upward coordinates, is the azimuthal angle and is the angular velocity.

1. Assume the vertical component of the magnetic flux density is

where n is the field index and R is the reference orbit. Show the radial magnetic field with B _r = 0 at z = 0 is

2. Using the normalised radial and vertical coordinates

show that the equations of motion become

Where ₀ =v/R=eB ₀ /m is the angular velocity of the orbiting particle. Also show that stability requires:

r 2 z

z r

dp dp

mr er B , er B

dt dt

v / r

0 0 1

n z

R r R

B B B n ... ,

r R

z 0 r

r R

nB

B z B z

r R

r R / R and =z/R

2 0 1 n 0 , + n ₀ ² 0 0 n 1

University of Melbourne

Betatron part of a 35M Volt electron accelerator used in nuclear research

between 1959- 1989.

Jones

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Microtron

5

22 and also by E.M. McMillan at the University of California in late 1945 (McMillan, 143).

The principle behind a microtron is similar to that of a cyclotron, but it is designed to accelerate electrons vice positive ions. The electrons pass through a circular orbit, each of which are all tangent to one another within the RF cavity. Each successive orbit is

longer than the one proceeding it such that

where the frequencies of revolution follow the sequence

RF Cavity ^x

y

Extraction

1 l

2 l

3 l

4 l

5 l

6 l

Figure 8: Basic principle of a microtron.

, m

0

qB

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schwache Fokussierung

6

R.M. Jones, Physics of Particle Accelerators, PHYS 4722, Circular Accelerators Lecture, 2011.

22 Transverse Control: Weak Focusing

Particles injected horizontally into a uniform, vertical, magnetic field follow a circular orbit.

Misalignment errors and difficulties in perfect injection cause particles to drift vertically and radially and to hit walls.

A severe limitations on machine operation

Require some kind of stability mechanism.

Vertical focusing from non-linearities in the field (fringing fields). Vertical stability requires

negative field gradient. But radial focusing is

reduced, so effectiveness of the overall focusing is limited.

r r if

v m

v qBv m

2 0

i.e. horizontal restoring force is towards the design orbit.

1 0 d

dB n B

Stability condition:

Weak focusing: if used widely today, scale of magnetic components of a synchrotron would be large and costly

Transverse Control:

Weak Focusing

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Synchrotron

7

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Linearbeschleuniger

36

Synchrotron Oscillations Series of accelerating cavities in: (a) synchr otr on and (b) a linac ^RF

accelerating cavities

RF accelerating cavity In principle, synchrotrons or linacs are designed such that the synchronous particle is accelerated continuously. In practice, non- synchronous particles will require acceleration too! Thus, the question of phase stability , or do particles with different energies and phases remain close to the synchronous phase? L/ v

In order to d er iv e a n e q u at io n f or t h e p as sa ge o f n on -s yn ch ro n ou s p ar ti cl e t h ro u gh t h e accelerator we consider the time interval between passages of two successive modules of accelerating cavities (or sometimes called accelerating stations): where L is the distance between stations and v the particle velocity v:

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SLAC, Stanford

9

68 Linacs

Linacs soon!

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Teilchenoptik und Phasenstabilität

25

Sextupoles are used to correct longitudinal momentum errors.

SLAC quadrupole

Focusing Elements

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“FODO” – Fokussierung

11

24

in

out

1 1 1 0

x x x f

x

f

x x

Effect of a focussing thin lens can be

represented by a matrix In a drift space of

length , x is unaltered

but x x+ x _out 0 1 _in

1 x x l

x x

In an F-drift-D system, combined effect is...

l f l f

f l l f

l

f 1

1 1 1

0 1

1 0

1 1 1

0 1

2

out in 2

1 0 x

l f

f x x l

Thin lens of focal length f ² / is focusing overall, if f.

Same applies for D-drift-F ( f - f )

Thus, a system of AG lenses can focus in both planes simultaneously!

“FODO” lattices of this form are almost always used...

Thin Lens Analogue of AG Focusing

D---drift---F

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Kollider: e ⁺ e ^– , ep, p(bar)p

12

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Beamlines at ANKA 29

Synchrotronstrahlung

14

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Livingston-Diagramm

15

1930 2010

Gleichrichter mit

Spannungsvervielfacher Elektrostatischer Generator

Zyklotron mit Sektorfokusierung

Protonen-Linearbe- schleuniger

Elektronen-Linearbe- schleuniger

Synchrozyklotron ISR

Elektronensynchrotron starke

Fokusierung

Starke

Fokusierung schwache

Fokusierung

schwache Fokusierung

Protonensynchrotron Speicherringe

(Äquivalent-Energie)

Sp Sp

Tevatron LHC ?

SSC ?

100 keV 1 MeV 10 MeV 100 MeV 1 GeV 10 GeV 100 GeV 1 TeV 10 TeV 100 TeV 1000 TeV 10000 TeV 100000 TeV

1940

Beschleunigerenergie(Laborsystem)

1950 1960 1970 1980 1990 2000 Betatron

Zyklotron

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10

⁰

10

^–2

10

^–4

10

^–6

10

^–8

10

^–10

10

¹⁰

10

¹²

10

¹⁴

10

¹⁶

10

¹⁸

10

²⁰

LHC ^GZK?

Flux x Ener gy

2

[r el at iv e u ni ts ]

Energy [eV]

knee

ankle

balloons, satellites

air showers

1/(m

²

s

⁾

1/(km

²

y

⁾

1/(km

²

100y)

LHC bea

Energiespektrum der kosmischen Strahlung

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Energy [eV/particle]

10

13

10

¹⁴

10

¹⁵

10

¹⁶

10

¹⁷

10

¹⁸

10

¹⁹

10

²⁰

]

1.5

eV

-1

sr

-1

s

-2

J(E) [m

2.5

Scaled flux E

10

13

10

14

10

15

10

16

10

17

10

18

10

19

[GeV]

s

pp

Equivalent c.m. energy

10

2

10

³

10

⁴

10

⁵

10

⁶

RHIC (p-p) -p) HERA (

Tevatron (p-p) LHC (p-p)

ATIC PROTON RUNJOB

KASCADE (QGSJET 01) KASCADE (SIBYLL 2.1) KASCADE-Grande 2009 Tibet ASg (SIBYLL 2.1)

HiRes-MIA HiRes I HiRes II Auger 2009

17

Energiespektrum und Schwerpunktsenergie

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log(R/cm)

log(B/G)

15

10

5

0 –5

–10 5 10 15 2 0 2 5 3 0

15

10

5

0 –5

–10 5 10 15 2 0 2 5 3 0

Neutron Stars

Active Galactic Nuclei

White Dwarfs

others

Protons Iron

Galactic

Disk Galactic Halo

Radio Lobes

Galaxy Clusters Gamma Ray Bursts

SNR

1 kpc

1 pc 1 Mpc

100 T eV

100 Ee V

Hillas condition and diagram:

E max ~ ß Z B L

Hillas-Diagramm

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Galaktische kosmische Beschleuniger

19

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Extragalaktische kosmische

Beschleuniger

20

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IKP in KCETA KT2012 Johannes Blümer

v3 24. April 2012

3

Detektoren 1

Wechselwirkung von Teilchen und Strahlen mit Materie; experimentelle Methoden

Detektoren 2

Detektorbaukasten; Grossdetektoren; andere

Anwendungen

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P = (E, p) !

Was wollen wir messen?

4

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Systematik

5

Kern- und Teilchenphysik SS2012

www.kit.edu

www.kit.edu

Kern- und Teilchenphysik SS2012

Johannes Blümer

Themen und Inhalte der Vorlesung

Inhalt

http://www.auger.de/~rulrich/lehre/kerneteilchen2012/index.html

Betatron

2

2

1 2 1 1

2 B p

qr

p E d

B r,t

qr r r dt

B r,t B dS

r

19 19

1. Particles accelerated by the rotational electric field generated by a time varying magnetic field.

2. In order that particles circulate at constant radius: dt E d

r

S d dt B

l d d E

t E B

2

B-field on orbit is one half of the average B over the circle. This

imposes a limit on the energy that can be achieved. Nevertheless the

constant radius principle is attractive for high energy circular accelerators.

Oscillations

about the design orbit are called betatron

oscillations

Magnetic flux,

Generated E-field

r

Betatron

Kerst and Serber built the first Betatron (1941)

Jones

R.M. Jones, Physics of Particle Accelerators, PHYS 4722, Circular Accelerators Lecture, 2011.

20

Betatron Motion

Exercise 2: As the oscillations from the design orbit in almost any accelerator are referred in terms of “betatron”

motion it is clearly important to understand this phenomena. Unsuprisingly, it was originally ascribed to oscillation in a betatron, but the name stuck!

In cylindrical coordinates the equation of motion for electrons is:

Where r and z refer to radial outward and vertical upward coordinates, is the azimuthal angle and is the angular velocity.

1. Assume the vertical component of the magnetic flux density is

where n is the field index and R is the reference orbit. Show the radial magnetic field with B r = 0 at z = 0 is

2. Using the normalised radial and vertical coordinates

show that the equations of motion become

Where 0 =v/R=eB 0 /m is the angular velocity of the orbiting particle. Also show that stability requires:

r 2 z

z r

dp dp

mr er B , er B

dt dt

v / r

0 0 1

n z

R r R

B B B n ... ,

r R

z 0 r

r R

nB

B z B z

r R

r R / R and =z/R

2

0 1 n 0 , + n 0 2 0 0 n 1

University of Melbourne

Betatron part of a 35M Volt electron accelerator used in nuclear research

between 1959- 1989.

Jones

Microtron

22

and also by E.M. McMillan at the University of California in late 1945 (McMillan, 143).

The principle behind a microtron is similar to that of a cyclotron, but it is designed to accelerate electrons vice positive ions. The electrons pass through a circular orbit, each of which are all tangent to one another within the RF cavity. Each successive orbit is

longer than the one proceeding it such that

where the frequencies of revolution follow the sequence

2. In order that particles circulate at constant radius: ^dt E d

where n is the field index and R is the reference orbit. Show the radial magnetic field with B _r = 0 at z = 0 is

Where ₀ =v/R=eB ₀ /m is the angular velocity of the orbiting particle. Also show that stability requires:

0 1 n 0 , + n ₀ ² 0 0 n 1

RF Cavity ^x

Synchrotron Oscillations Series of accelerating cavities in: (a) synchr otr on and (b) a linac ^RF

but x x+ x _out 0 1 _in