Appendix A Gyrotron Theory

A.1 Calculation Procedure

The gyrotron is a maser device for which the underlying mechanism is normally understood within the frame work of quantum mechanics as based on transitions between Landau levels rather than using transitions between atomic levels. From this perspective, gyrotrons are more specifically cyclotron masers. However, describing the gyrotron mechanism quantum mechanically is not practical. Instead, classical considerations using Maxwell’s equations and the Lorentz force are usually used [1, 2] and give a satisfactory understanding of gyrotron behavior. First, we introduce electromagnetic fields into the RF cavity in the absence of an electron beam. Electron- beam handling is then discussed. Next, the interactions between the millimeter waves and the electron beam are calculated. This formalism is called the cold cavity method, in which perturbations from the electrons to the profile of the radiation field is ignored. Another formalism, called the self consistent method, enables the electron motion and RF behavior to be solved simultaneously. The cold cavity formalism is a good approximation when the quality factor of the RF cavity is sufficiently high.

A.2 Theory of the RF Cavity

The RF cavity is an open-ended cylindrical resonator that has a characteristic angular frequency of resonance, which we denote by ωr. The resonator can be thought of as an irregular waveguide because the radius (R) of the helical motion of the electrons varies slowly along the z-axis as plotted in Fig. A.1. Electrons from the MIG are introduced, where the resonator is cut off (left-hand side of figure), preventing RF fields from leaking and damaging the MIG. The intermediate region constitutes a flat waveguide of radius R2 and length L2. The output section (right-hand side of figure) is open.

© Springer Japan 2015 97 A. Miyazaki, Direct Measurement of the Hyperfine Structure Interval of Positronium Using High-Power Millimeter Wave Technology, Springer Theses, DOI 10.1007/978-4-431-55606-0 98 Appendix A: Gyrotron Theory

Fig. A.1 Cross-sectional geometry of the RF cavity used in the gyrotron FU CW GI

The resonance mode of the RF cavity is a solution to Maxwell’s equations in a cavity wall. We shall use cylindrical coordinates, (r,φ,z) in accordance with the symmetry of the cavity. Only the transverse electric (TE) modes are considered because gyrating electrons couple to the transverse electric fields and not with the magnetic fields. Upon introducing an azimuthal index (m = 0, ±1, ±2, ±3, ···), a radial index (n = 1, 2, 3, ···), and an axial index (l = 1, 2, 3, ···), the eigenmodes of this cavity (TE resonance modes) are products of a transverse vector function, −→ mnl E (r,φ) and an axial scalar function, (z). One can approximate the transverse −→ electric field ( E (r,φ))bytheTEmn modes propagating through a circular waveguide, expressing them as:   R j E (r,φ)= E m J mn r sin(mφ), (A.1) r 0 r m R     jmn Eφ(r,φ)= E J r cos(mφ), (A.2) 0 m R

Ez(r,φ)= 0, (A.3) where E0 is the normalized strength of the electric field, Jm(x) the m-th Bessel  ( )   ( ) = function of the 1st kind, Jm x its 1st derivative, and jmn is the n-th root of Jm x 0. As the taper angles of the cavity are small, the changes in R(z) can be ignored and −→ mode mixing with other TEmn s is also negligible. FigureA.2 gives E (r,φ)for the TE52 used in this experiment. Note that there are two degenerated states according to the sign of the azimuthal index (m), except for when m = 0, which corresponds to a phase rotation around the z-axis. When gyrating electrons are present, this degeneracy is removed and the electron motion becomes either co-rotating or counter-rotating with respect to the magnetic field. Appendix A: Gyrotron Theory 99

Fig. A.2 Transverse 3 structure of the electric field in the RF cavity (TE52 mode) 2

1

0 y [mm]

-1

-2

-3 -3 -2 -1 0 1 2 3 x [mm]

The axial function ((z)) obeys the equation describing a nonuniform string:

d2(z) + ζ 2 (z)(z) = , 2 mn 0 (A.4) dz      ω 2 j 2 ζ (z) = − mn , (A.5) mn c R(z)   where ω = ω 1 + i is the complex RF frequency and Q the diffraction r 2QD D quality factor. Corrections for the open-endedness of the cavity were calculated for the cutoff and output sections to estimate ωr and QD simultaneously. Equation (A.4) can be solved numerically under the following boundary conditions:

d (0) = iζ  (A.6) dz mn d (z ) =−iζ , (A.7) dz out mn where zout is the end-point of the output taper (zout = L1 + L2 + L3). Equation (A.4) can be solved using Eq. (A.6) as the initial condition, for example, using the Runge-Kutta formula. Next, the two variables (ωr, QD) are varied until the sec- ond boundary condition, Eq. (A.7), is satisfied. FigureA.3 shows the result of this calculation for the RF cavity used in this experiment. The three different curves cor- respond to different axial indices (l = 1, 2, 3). The solutions are listed in Table A.1. The quality factor from the Ohmic loss (Q) and the combined Q are also shown. 100 Appendix A: Gyrotron Theory

120

100

80

60 (z) [a.u.] Ψ 40

20

0 0 5 10 15 20 25 z [mm]

Fig. A.3 Axial structure of the electric field in the RF cavity. The solid, dotted,anddashed lines show the TE521,TE522 and TE523 modes, respectively

Table A.1 Resonance frequency and QD of the three modes shown in Fig. A.3 Mode Frequency (GHz) QD Q Q

TE521 203.01 3200 10600 2500 TE522 203.59 810 10600 750 TE523 204.56 380 10600 370

The cavity parameters are (L1, L2, L3) = (5, 14, 5mm) and (R1, R2, R3) = (2.345, 2.475, 2.735 mm)

The Ohmic quality factor is given by:    R2 m Q = − , δ 1  (A.8) jmn where δ = 0.18 µm is the skin depth of copper at 200 GHz. Under normal operations of the gyrotron (gyromonotron), the TE521 mode (the solid line in Fig. A.3) is excited. Interactions with the backward-wave are needed for the electrons to couple to higher axial modes. This device is called a gyro-BWO and has the potential to continuously tune the output frequency. The output power of this device is currently less than 100 W, which is insufficient to measure the Ps-HFS. A proposal on how to achieve higher power is suggested in the future prospects section (Sect. 4.3).

A.3 Theory of the Electron Beam

An electron beam should be properly controlled and introduced into the correct position in the RF cavity to obtain maximum coupling between electrons and RF Appendix A: Gyrotron Theory 101

fields. A sophisticated method to control the electrons has been developed in gyrotron physics. The simplest approximation is described in this section. Electrons are emitted from an emitter ring at the cathode and are accelerated between the 1st and 2nd anodes (Fig.2.2). Guided by the magnetic field, they enter the RF cavity and gyrate where the magnetic field strength is maximal at about 7.5 T (Fig. A.4). Finally, the electron beam is dumped by a beam collector (Fig. 2.2). FigureA.5 shows the electron trajectories simulated using CST PARTICLE STU- DIO [3]. The radius of the electron beam is compressed by the strong magnetic field in the cavity. Depending on the beam radius (Rb), electrons maximally couple to one specific mode (TEmn1) in the RF cavity, as described in Sect. A.2. This coupling strength is determined by the function:

8

7

6

5

4 Bz [ T ] 3

2

1

0 0 200 400 600 800 1000 z [mm]

Fig. A.4 Simulated magnetic field (Bz) along the z-axis (simulated using CST PARTICLE STU- DIO). The emitter ring is at z =0 mm and the RF cavity is at 650mm

Fig. A.5 Simulated electron trajectories from the MIG (simulated using CST PARTICLE STUDIO) 102 Appendix A: Gyrotron Theory

Fig. A.6 Coupling factor of the TE52 mode. The solid 0.025 line represents the counter-rotating mode and 0.02 the dashed line the co-rotating mode 0.015 G

0.01

0.005

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Rb/R

2  J ∓ j Rb/R G = m 1 mn , (A.9) mn ( 2 − 2) 2 ( 2 ) jmn m Jm jmn where the sign of m ∓1 signifies either co-rotating or counter-rotating wave propaga- tion relative to the direction of the electron gyration. FigureA.6 shows the calculated G52. It is clear that the degeneracy of the co- and counter-rotating modes is removed. When the gyrotron oscillator is operated in the counter-rotating TE52 mode, Rb should be controlled so that the wave covers 0.7 of the cavity radius R2. Depending on magnetic field strength, the beam radius (Rb) is compressed, as demonstrated in Fig.A.5. This adiabatic compression is expressed as:  Bc Rb(z) = Rc, (A.10) Bz(z) where Bc ∼ 0.1 T is the z−component of the magnetic field at the emitter ring at the cathode, and Rc ∼ 14 mm is the ring radius (Fig. 2.2). The factor b = Bz(z)/Bc is called the compression ratio. Bc can be optimized by introducing a normal conducting gun-coil solenoid around the MIG so that the size of Rb is more adapted to the counder-rotating modes (i.e., 0.7 of the cavity radius). −→ −→ The magnetic field induced by the gun-coil also affects the E × B drift near the −→ −→ −→ cathode [4]. The E × B drift determines the initial perpendicular velocity ( v ⊥c) of the electrons emitted thermally from the cathode surface

EcφEB v⊥c ∼ , (A.11) Bc where E is the electric field strength at the cathode and φ is the angle between −→ c−→ EB E c and B c. Ec is controlled by the voltage difference between the cathode (Vk ∼ −18 kV) and the 1st anode (V ∼−10 kV). The electrons start gyrating because of −→ −→ a this E × B drift. Appendix A: Gyrotron Theory 103

In accordance with the adiabatic approximation, the magnetic momentum 2 (mev⊥/Bz) is constant [4]. Therefore, v⊥ becomes increasingly faster along the trajectory, in correspondence with the increasing magnetic field (Fig.A.4). The veloc- 2 2 ity parallel to Bz, v// = v − v⊥ is correspondingly reduced in the RF cavity because the total energy is conserved. The energy of the cyclotron radiation increases 2 proportionally to v⊥. The optimum value of the velocity ratio, α = v⊥/v// (called pitch factor) at the cavity ranges from 1.2 to 1.5. The pitch factor is controlled using the magnetic field of the gun-coil and the voltage of the 1st anode.

A.4 Excitation Theory

So far, the RF fields in the RF cavity have been obtained and the optimum electron beam was introduced into the RF cavity. We shall now calculate their interactions and consider the excitation conditions in the gyrotron [1]. Steady-state operations will be our focus of interest. The gyrotron oscillation can be estimated by calculating the electron motion affected by the Lorentz force from the RF fields described in Sect. A.2. In general, the equation of the motion for electrons is:

dE −→ −→ =−e v · E (A.12) dt −→ d p −→ e −→ −→ =−e E − v × B , (A.13) dt c

2 where E = γ mec is the relativistic energy of an electron. One can consider Eq. (A.13) in a coordinate system with the origin at the electron −→ iθ gyrocenter. In complex notation, p → px+ipy = pe , where θ is the relative phase between the momentum of an electron and an electromagnetic wave in momentum space. The electron energy and momentum was normalized by the initial energy 2 before the interaction (denoted as γ0mec ). If it is assumed that the propagating velocity in the RF cavity is constant and the independent variable can be transformed from time to a normalized axial position, this can be expressed as:

2 β⊥ωc ζ = z. (A.14) 2β//c −→ With the small argument expansion of the Bessel functions in E (r,φ), the resulting equation for the motion is:   dp (ζ) + ip +|p|2 − = iG , ζ 1 (A.15) d ||2dζ 104 Appendix A: Gyrotron Theory where is the frequency detuning, defined as:   2 ω − ω = r c , (A.16) 2 ω β⊥ r and G is the coupling parameter, defined as:  1 Q · P = . × −3 D out . G 0 47 10 2 Gmn (A.17) 2 γ0Vkηelβ//β⊥

The acceleration voltage (Vk, cathode voltage), output power (Pout), and electron efficiency, 2 β⊥ ηel = (A.18) 2(1 − 1/γ0) were also introduced. The steady-state gyrotron oscillation is obtained by solving Eq. (A.15)foragiven Pout. Note that Pout determines the absolute value of the RF field, which is calculated without a source term in the cold cavity formalism. The results of Eq. (A.15)forsome electrons in different phases are shown in Fig. 2.4. The orbital efficiency was obtained by averaging the results of the electrons initially in different phases p j (0) = exp (iθ j ) (0 <θj < 2π, j = 1, 2, ···, N,)   1  2 η⊥ = 1 − p (ζ ) . (A.19) N j out j

Then, the electron-beam current (Ib) required to achieve a given Pout was calculated using:

2.5

2

1.5 [kW] out

P 1

0.5

0 7.38 7.4 7.42 7.44 7.46 B [T]

Fig. A.7 Calculated output power of the gyrotron. The operation parameters are the cathode voltage (Vk =−18 kV), beam current (Ib = 500 mA), magnetic field (B = 7.4 T), cavity radius (R2 = 2.475 mm), beam radius (Rb = 0.7 · R2), and pitch factor (α = 1.2) Appendix A: Gyrotron Theory 105

Fig. A.8 Oscillation efficiency vs beam current. The left plot corresponds to soft excitation and the right to hard excitation. The solid line shows the oscillation with the same magnetic field or frequency detuning

Q Pout = Vk · Ib · η⊥ · ηel · . (A.20) Q + QD

This is the energy conservation condition between the electron beam and the RF field. The RF field gained energy from the electrons, calculated using Equations (A.15) and (A.19). FigureA.7 shows an example of the solution for different magnetic field strengths. The output power rises rapidly and then gradually decreases as the magnetic field strength is increased. This is typical behavior of a gyrotron oscillator.

A.5 Soft and Hard Excitation

There are two oscillation conditions: soft excitation (ωc ≤ ωr) and hard excitation (ωc  ωr). FigureA.8 show the calculations of the oscillation efficiency (η = η⊥·ηel) for these two conditions. η is a single-valued function of Ib in the soft excitation con- dition (left figure) but is a multivalued function of Ib in the hard excitation condition (right figure). High powers are obtained in the hard excitation condition. A difficulty of the hard excitation is that the gyrotron starts to oscillate at large Ib values, and η increases as Ib decreases untill reaching the minimum possible value. After η exceeds ∼ 0.1, η increases as Ib increases. Stabilization of the output power with a simple feed-back control is difficult because of the non-linear behavior of the gyrotron (see Sect. 2.2.4). Moreover, two different η values for the same Ib and B0 (the same oper- ation conditions) can cause a sudden jump in the output power without changing any external parameters. Careful operations are generally required in the hard excitation condition. 106 Appendix A: Gyrotron Theory

Fig. A.9 Dependence of Ist on the displacement. The left plot shows Ist with perfect alignment. The right plot shows Ist with a displacement of 0.5 mm

A.6 Alignment Effect

Gyrotron oscillations are sensitive to the displacement between the RF cavity and the electron beam. We introduced a starting current (Ist) that was the smallest electron- beam current required for gyrotron oscillations [2]. Ist can be calculated using the method described in Sect. A.4 with Pout > 0. Changing Ist by a displacement (d mm), which is expressed as: [5]

2 2π · Jm±1 λ Rb Ist(d) = Ist(0) ∞    . (A.21) 2π 2π J 2 · d · J 2 · R q λ m−q±1 λ b q

The results of the calculation are shown in Fig.A.9. When there is no displacement (left), only the counter-rotating TE52 mode oscillates, when B0 = 7.45 T and Ib = 0.4 A (the same conditions as this experiment). For a displacement of 0.5 mm (right), the structure of Ist changed and both the counter-rotating and co-rotating TE52 modes satisfy Ist > Ib = 0.4 A. These two modes compete with each other, reducing the efficiency of the electron phase bunching (mode competition). Consequently, careful alignment better than 0.5mm is required to obtain a high-power gyrotron output. This is technically difficult because the size of the gyrotron is rather large (Fig. 2.2). This is one of the reasons for the poor reproducibility of the gyrotron operation (Table 2.2). Note that the gyrotron previously used in this experiment [6] was operated in the TE03 mode, for which the counter- and co-rotating modes are degenerate. Hence no mode competition occurred. The previous gyrotron was insensitive to the displacement. We selected the TE52 mode because the conversion efficiency of the Gaussian mode converter is better than that of the TE03 mode. The principle of the converter is described in the next section. Appendix A: Gyrotron Theory 107

Fig. A.10 Rays of the time-averaged propagating TEmn mode in a waveguide.

A.7 Theory of the Gaussian Mode Converter

The output from the gyrotron RF cavity was the TEmn mode in a circular waveguide. This needed to be converted to a linearly polarized Gaussian beam (TEM00 mode) for accumulation in the Fabry–Pérot cavity [7]. This was achieved using a Gaussian mode converter that was developed for application in plasma heating. When we consider the time-averaged Poynting vector using Eq. (A.1), the energy flux of the TEmn modes can be treated as rays bouncing along the inside walls of a waveguide in a polygonal helix, as depicted in Fig. A.10. This diagram shows that the TEmn modes could be decomposed into a series of linearly polarized (helically rotating) plane waves. The envelope of the helically reflecting rays in a waveguide with radius RW becomes a cylindrical caustic with radius RC,

= × m . RC RW  (A.22) jmn

For the TE52 mode, we used a value of RC that was 0.475 of RW. The waveguide opening should be cut open in a helical shape with the helical cut following the ray trajectories in the waveguide. Figure A.11 gives a perspective view of the helical launcher used in this experiment. The radiation launched from the helical antenna expanded in a radial and twisted fashion, corresponding to the helical rotation in the waveguide. A quasi-parabolic reflector was introduced to focus 108 Appendix A: Gyrotron Theory

Fig. A.11 Three- dimensional view of the helical launcher.

the radiation and to shape its profile. The left diagram in Fig.A.12 shows a top view of the launcher and the reflector. The reflector shape was calculated assuming that the optical path lengths for all rays between the phase front and the focal point were equal. For parallel light (focal point at infinity), the parametric representation (xr, yr) of the reflector shape can be expressed [7] as:   1 xr(φ) = RC − (2 f0 − RCφ) tan φ (A.23)    2     1 1 1 y (φ) = R tan φ − f − R φ tan2 φ − 1 , (A.24) r C 2 0 2 C 2 where f0 is the maximum value of yr and φ is a parameter. For m = 0, in particular, the caustic radius (RC = 0) and the reflector shape become

=− 1 2 + . yr xr f0 (A.25) 4 f0

This type of reflector was used in the previous experiment, where the oscillation mode was TE03 [6]. The shape of m = 0 was similar to a parabola (quasi-parabola). The reflected rays made up the linearly polarized beam of which the electric field vectors were parallel to the x-axis, as shown in the left diagram of Fig.A.12. The right diagram in Fig. A.12 shows a side view of the launcher and the reflector. The propagating angle (θB) is called the Brillouin angle and is defined as:    λ −1 jmn θB = sin . (A.26) 2π RW

The axial structure should be fabricated so that the reflected rays do not hit the launcher head for all of the frequencies used. Appendix A: Gyrotron Theory 109

Fig. A.12 Schematic of the Gaussian converter. (left) Top view. (right) Side view

A linearly polarized bi-Gaussian beam can be made with the launcher and the quasi-parabolic reflector. Two additional plane mirrors, located over the reflector, extract the beam from a small bore in the superconducting solenoid (Fig. 2.2). An ellipsoidal mirror re-shapes the beam and focuses it near the output window.

References

1. O. Dumbrajs, T. Idehara, T. Saito, Y. Tatematsu, Jpn. J. Appl. Phys. 51, 126601 (2012) 2. B.G. Danly, R.J. Temkin, Phys. Fluids 29, 561 (1986) 3. C.C.S.T. AG, CST Particle Studio (2011), http://www.cst.com 4. F.F. Chen, Introduction to Plasma Physics (Plenum Press, New York, 1974) 5. O. Dumbrajs, Int. J. Infrared Millim. Waves 15, 1255 (1994) 6. T. Yamazaki, A. Miyazaki, T. Suehara, T. Namba, S. Asai, T. Kobayashi, H. Saito, I. Ogawa, T. Idehara, S. Sabchevski, Phys. Rev. Lett. 108, 253401 (2012) 7. C.J. Edgcombe, Gyrotron Oscillators (Taylor and Francis, London, 1993) Appendix B Theory of Positron Acceleration

B.1 Toy Model for the Interactions

The interaction between a positron, an oscillating electric field E0 sin (ωt), and gas molecules can be described by the following differential equation:

dv m = eE sin (ωt) − mω v, (B.1) e dt 0 c where v is the positron velocity, ωc the average angular frequency of the collisions, and mωcv the relaxation term for the collisions. An analytical solution for Eq. (B.1) is:     eE 1 − ω v(t) = 0 sin ωt − tan 1 . (B.2) ω2 + ω2 ω me c c

The estimate for the mean energy gain (δE) during the collision cycle τc is obtained from  =τ t c e2 ω2 δE = eE(t)v(t)dt = c × E2. (B.3) ω2 ω2 + ω2 0 t=0 2me c c

Ina1atmnitrogen gas witha1eVpositron,τc is approximately 3.3 ps. With 203 GHz millimeter waves, the expected energy gain of the positron is:   2 −1 δE ∼ 0.51 meV × E0/100 kVm (B.4) per collision. This is very small compared with the Ore gap.

© Springer Japan 2015 111 A. Miyazaki, Direct Measurement of the Hyperfine Structure Interval of Positronium Using High-Power Millimeter Wave Technology, Springer Theses, DOI 10.1007/978-4-431-55606-0 112 Appendix B: Theory of Positron Acceleration

B.2 Random Walk Model

A sequence of collisions can be modelled using a random-walk model. As the mil- limeter wave radiation in the Fabry-Pérot resonant cavity was linearly polarized, it suffices to consider a one-dimensional random walk model. If the collisions are suf- ficiently random and are not correlated with the oscillation of the electric field, the probability distribution of v after n collisions is expressible in the form   1 (v − v )2 g(v) = √ exp − 0 , (B.5) πσ 2σ 2 √2 σ = nδv, (B.6) where v0 is the initial velocity of a slow positron (a few eV), and δv the acceleration or deceleration per collision determined by δv = 2meδE. What we are interested in is the probability of exceeding the lower edge of the Ore gap (Ethr = I − 6.8eV). If vthr denotes the corresponding positron velocity, this probability can be calculated using  vthr G(v > vthr) = 1 − g(v)dv. (B.7) −vthr

FigureB.1 shows G(v > vthr) in the 1 atm nitrogen case (Ethr ∼ 7.7 eV). The power dependence is related to δE, which is determined by the gas scattering properties. Previous experiments have studied the effect of static electric fields using Boltzmanns equation [1, 2]. One can also construct Monte Carlo simulations to model this phenomenon. Even with these seemingly more quantitative approaches, uncertainties in the inelastic scattering need to be determined through fitting the data. Comparisons between the models and data need many data points at different accumulated powers. This is difficult with the present stability of the gyrotron.

Fig. B.1 Simulated Ps 100 formation dependence on power. Calculations with 80 different δE0 values are plotted 60 δ E0 = 0.05 meV

G [%] δE = 0.1 meV 40 0 δ E0 = 0.5 meV δ 20 E0 = 1.0 meV δ E0 = 5.0 meV 0 020406080100120

Pacc [kW] Appendix B: Theory of Positron Acceleration 113

References

1. S. Marder, V.W. Hughes, C.S. Wu, W. Bennett, Phys. Rev. 103, 1258 (1956) 2. W.B. Teutch, V.W. Hughes, Phys. Rev. 103, 1266 (1956) Appendix C Data Summary

The quantities recorded at the main trigger timing are summarized in TableC.1.The quantities recorded in synchronization with the gyrotron output pulse are summa- rized in TableC.2. The quantities monitored with the interlock are summarized in TableC.3.

Table C.1 Quantities measured at the main trigger timing Name Module Event ID - Real time - Gyrotron ON/OFF Input register (LeCroy C005) Pla-energy (short gate), 2ch CS ADC (PHILLIPS 7167) Pla-energy (long gate), 2ch CS ADC (REPIC RPC-022) La-energy, 4ch CS ADC (CAEN C1205) Pla-time, 2ch TDC (KEK GNC-060) La-time, 4ch TDC (KEK GNC-060) Live time SCALER (Kaizu KC3122) Pla-rate, 2ch SCALER (Kaizu KC3122) Pla-and-rate SCALER (Kaizu KC3122) La-rate, 4ch SCALER (Kaizu KC3122)

© Springer Japan 2015 115 A. Miyazaki, Direct Measurement of the Hyperfine Structure Interval of Positronium Using High-Power Millimeter Wave Technology, Springer Theses, DOI 10.1007/978-4-431-55606-0 116 Appendix C: Data Summary

Table C.2 Quantities recorded in synchronization with the gyrotron output pulse Name Device Input power Pyroelectric detector Reflected power Pyroelectric detector Transmitted power Pyroelectric detector Trigger pulse of gyrotron ADC (NI USB-6215) Beam current of gyrotron ADC (NI USB-6215) Heater voltage of the MIG (input parameter) Cavity length NANO CONTROL TS102-G Room temperature Logger (HIOKI 8420-50) Temperature of NIM bin Logger (HIOKI 8420-50) Temperature in the gas chamber Logger (HIOKI 8420-50) Pressure in the gas chamber Logger (HIOKI 8420-50)

Table C.3 Quantities monitored with the interlock Name Reason Temperature of the collector Check abnormal electron beam operation Temperature of the gyrotron body Check abnormal electron beam operation Temperature of the flange on the MIG Check abnormal electron beam operation Temperature of the output window Protect window glass Vacuum of the gyrotron Protect the emitter surface of the MIG Water flow for gyrotron cooling Protect gyrotron vacuum vessel Water flow for chamber cooling Prevent the mesh mirror from melting Appendix D Small Systematic Uncertainties

The efficiency of the accidental rejection and background normalization were negli- gible when calculating the Ps-HFS compared with the other errors. The differences were small but significant. They are listed in Tables D.1 and D.2 for future pre- cise measurements. They may have been caused by electric noise during the pulsed operation of the gyrotron (voltage =−18 kV, current = 500 mA, width =60ms, frequency=5Hz). RUNs in which the Fabry-Pérot cavity was off-resonance (−0) are also shown as a reference.

Table D.1 Accidental rejection efficiencies RUN ID Efficiency (beam Efficiency (beam Difference% ON)% OFF)% A-1 56.544(76) 56.486(50) 0.10333(17) A-2 56.916(77) 56.973(51) −0.09990(16) B-0 52.083(86) 52.179(56) −0.18416(36) B-1 52.574(65) 52.570(43) 0.00799(1) C-0 56.464(96) 56.362(65) 0.18097(37) C-1 56.156(69) 56.283(63) −0.22565(38) C-2 54.35(10) 54.370(66) −0.03678(8) C-3 56.576(79) 56.614(52) −0.06712(11) D-0 54.46(13) 54.418(87) 0.07673(22) D-1 53.047(73) 53.060(48) −0.02458(4) D-2 54.69(18) 55.07(12) −0.6838(27) D-3 54.41(18) 54.40(11) 0.01758(7) D-4 54.34(17) 54.45(11) −0.20478(78) D-5 54.63(19) 54.69(12) −0.11336(47) (continued)

© Springer Japan 2015 117 A. Miyazaki, Direct Measurement of the Hyperfine Structure Interval of Positronium Using High-Power Millimeter Wave Technology, Springer Theses, DOI 10.1007/978-4-431-55606-0 118 Appendix D: Small Systematic Uncertainties

Table D.1 (continued) RUN ID Efficiency (beam Efficiency (beam Difference% ON)% OFF)% E-0 54.580(93) 54.590(61) −0.01841(4) E-1 54.434(92) 54.402(60) 0.05929(12) E-2 55.143(90) 55.025(60) 0.21576(42) F-0 56.10(14) 56.104(92) −0.002552(8) F-1 56.381(69) 56.258(45) 0.21881(32) F-2 52.779(72) 52.732(47) 0.08910(14) G-0 55.217(65) 55.146(43) 0.12797(18)

Table D.2 Normalization of RUN ID Livetime s Uncertainty% the uncertainties A-1 6.7 × 104 0.07 A-2 6.7 × 104 0.07 B-0 7.0 × 104 0.08 B-1 1.1 × 105 0.06 C-0 7.2 × 104 0.08 C-1 6.6 × 104 0.08 C-2 6.8 × 104 0.08 C-3 9.9 × 104 0.07 D-0 2.6 × 104 0.07 D-1 7.2 × 104 0.12 D-2 1.2 × 104 0.17 D-3 1.3 × 104 0.16 D-4 1.4 × 104 0.15 D-5 1.3 × 104 0.16 E-0 2.3 × 105 0.08 E-1 6.1 × 104 0.08 E-2 6.0 × 104 0.09 F-0 5.8 × 104 0.12 F-1 1.0 × 105 0.06 F-2 8.0 × 104 0.07 G-0 1.2 × 105 0.06 Curriculum Vitae

Akira Miyazaki

Education & Academic Degree

2011–2014

PhD, The University of Tokyo. Department of Physics and International Center for Elementary Particle Physics 2009–2011

Master of Science, The University of Tokyo. Department of Physics and International Center for Elementary Particle Physics 2005–2009

Bachelor of Science, The University of Tokyo. Department of Physics

PhD thesis

Title

Direct Measurement of the Hyperfine Structure Interval of Positronium Using HighPower Millimeter Wave Technology Supervisor

Professor Shoji Asai

© Springer Japan 2015 119 A. Miyazaki, Direct Measurement of the Hyperfine Structure Interval of Positronium Using High-Power Millimeter Wave Technology, Springer Theses, DOI 10.1007/978-4-431-55606-0 120 Curriculum Vitae

Examiners

Professor Ryugo Hayano, Professor Sachio Komamiya, Professor Katsuo Tokushuku, Professor Takaaki Kajita and Professor Satoshi Yamamoto

Professional Experience

2014– CERN Fellow, The European Organization for Nuclear Research, Geneva. • A member of the ISOLDE grounp. Working on the HIE-ISOLDE project, upgrade project of particle energy using a compact superconducting linac. 2014 Project Researcher, The University of Tokyo, Tokyo. • Planning of future experiments using positronium. 2011–2014 Research Fellowship for Doctoral Course Student (DC1), Japan Society for the Pro- motion of Science (JSPS), Tokyo. • The first direct measurement of the positronium hyperfine structure.

Languages

Japanese (mother tongue), English (B2), French (A1)

Computer Skills

OS

LINUX, WINDOWS, MAC-OSX Office

MS-Word, Excel, Power Point Languages

C, C++, shell, perl, python Curriculum Vitae 121

CAD

Inventor, JW-CAD

Other softwares

ROOT, GEANT4, CST, ANSYS, Methematica

Research Interests

(i) Future accelerators. Understanding and constructing superconducting RF cavities. (ii) Elementary particle physics. Both high energy physics and precision tests (iii) Plasma physics. A dynamic interaction between plasma and electromagnetic- fields.

Invited Talks at International Conferences

(i) “First Spectroscopy of the Hyperfine Interval of Positronium Using Millime- ter Waves”, International Conference on Exotic Atoms and Related Topics (EXA2014) Sep. 15th 2014, Austrian Academy of Sciences, Wien, Austria (ii) “The direct spectroscopy of positronium hyperfine structure using sub-THz gyrotron”, International Symposium on Frontiers in THz Technology (FTT2012), Nov. 27th 2012, Nara, Japan

Invited Talks at School and Seminars

(i) “First Spectroscopy of the Hyperfine Interval of Positronium Using Millimeter Waves”, Seminar on Particle and Astrophysics at University of Zurich and Swiss Federal Institute of Technology Zurich (ETH), Dec. 10th 2014, Zurich, Switzerland (ii) “Direct measurement of the positronium hyperfine interval using millimeter waves”, International School of Subnuclear Physics – 52th Course, Jun. 24th – Jul. 3th, 2014, Erice, Sicily, Italy (iii) “First Direct Measurement of Positronium Hyperfine Splitting: New Particle Physics at a Frequency Frontier”, International School of Subnuclear Physics - 49th Course, Jun. 24th - Jul. 3th, 2011, Erice, Sicily, Italy 122 Curriculum Vitae

Awards

(i) “Honarable Mention for Young High Energy Physicists”, 2014, Japan Associ- ation of High Energy Physicists, The Physical Society of Japan (ii) “Giuseppe P.S. Occhialini diploma”, International school of subnuclear physics 52th course: STATUS OF THEORETICAL UNDERSTANDING AND OF EXPERIMENTAL POWER FOR LHC PHYSICS AND BEYOND, Erice, Sicily, Jun. 24th – Jul. 3th, 2014 (iii) “Encouragement Award for PhD Students”, 2013, Faculty of Science, The Uni- versity of Tokyo (iv) “First Place Out Standing Student Paper Award”, 36th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THZ 2011), Houston, Texas, USA, Oct. 2nd – 7th, 2011 (v) “New Talent Award in Experimental Physics” and “Isidor I. Rabi diploma”, In- ternational school of subnuclear physics 49th course: SEARCHING FOR THE UNEXPECTED ATLHC AND STATUS OF OUT KNOWLEDGE, Erice, Sicily, Jun. 24th – Jul. 3th, 2011 (vi) “New Talent Award in Detector Physics” and “Isidor I. Rabi diploma”, Inter- national school of subnuclear physics 48th course: WHAT IS KNOWN AND UNEXPECTED AT LHC, Erice, Sicily, Aug. 29th – Sep. 7th, 2010