Project 745: TinyML Superconducting RF Cavity Cold-Beam Vacuum Cryopump Inductive Superconducting Persistent Current Magnetic Field Harmonics Guard

Project 745: TinyML Superconducting RF Cavity Cold-Beam Vacuum Cryopump Inductive Superconducting Persistent Current Magnetic Field Harmonics Guard

1. 1.
   Executive Summary & Architectural Overview

Superconducting Radio-Frequency (SRF) linear accelerators rely on cryogenic cold-beam vacuum cryopumps to sustain ultra-high vacuum (P < 10^{-10}\ \text{mbar}) in the 2 Kelvin helium cryomodule. These cryopumps utilize high-field superconducting magnets operating in persistent current mode, where a closed superconducting loop (NbTi or \text{Nb}_3\text{Sn}) traps several hundred amperes without continuous external power input.

Maintaining beamline transmission fidelity requires the persistent magnetic field to possess extreme spatial homogeneity. Deviations in field geometry introduce unwanted multipole field harmonics:

Flux Creep & Pinning Center Decay: Due to thermal activation, magnetic flux vortices creep past pinning centers in the superconductor. This non-uniform flux decay distorts the spatial harmonic distribution, generating unwanted sextupole (b_3), octupole (b_4), and decapole (b_5) field harmonics that perturb electron/proton beam trajectories.

Persistent Current Quench Precursors: Before a thermal quench occurs, localized flux jumps generate sub-microvolt transient voltage pulses and harmonic field redistributions. Detecting these harmonic anomalies enables sub-millisecond quench dump triggering before stored magnetic energy vaporizes cryogenic helium.

Beam Vacuum Degradation: Spatial magnetic distortions alter the ion-trapping trajectories of the cryogenic pump, reducing pumping speed by up to 45% and risking residual gas ionization that induces SRF cavity field emission.

The TinyML Superconducting Persistent Current Magnetic Field Harmonics Guard is an edge-AI cryogenic monitoring instrument powered by an STM32F405RG (168 MHz ARM Cortex-M4 with Hardware FPU). It captures spatial magnetic field signals from a stationary 16-coil inductive pickup array positioned around the cryostat perimeter via an AD7606 16-bit 200 kSPS ADC. Running real-time discrete multipole expansion and an on-chip TinyML Autoencoder anomaly detection model, the instrument evaluates field harmonic distortion and triggers an ultra-fast quench dump within 1.0 ms.

+---------------------------------------------------------------------------------------------------+

| PROJECT 745: SRF FIELD HARMONICS GUARD BLOCK DIAGRAM |

+---------------------------------------------------------------------------------------------------+

| |

| [2 KELVIN LIQUID HELIUM CRYOMODULE: 4.5 TESLA PERSISTENT SUPERCONDUCTING CRYOMAGNET] |

| +-----------------------------------------------------------------------------------------+ |

| | 16-Channel Radial Inductive Pickup Coil Array (Coils C1 through C16 at 22.5 deg Spacing)| |

| | Cryogenic Cernox RTD Sensors & High-Purity Hall Probes | |

| +-----------------------------------------------------------------------------------------+ |

| | (16 Differential Microvolt Signals) |

| v |

| +-----------------------------------------------------------------------------------------+ |

| | Cryogenic Low-Noise Preamplifier & Instrumentation Stage (AD8429, Gain = 1000) | |

| +-----------------------------------------------------------------------------------------+ |

| | (0 - 5V Normalized Analog Waveforms) |

| v |

| +-----------------------------------------------------------------------------------------+ |

| | Dual Cascaded AD7606 8-Channel 16-Bit 200 kSPS Simultaneous ADCs (SPI Bus @ 20 MHz) | |

| +-----------------------------------------------------------------------------------------+ |

| | |

| v (DMA Ring Buffer Stream) |

| +-----------------------------------------------------------------------------------------+ |

| | STM32F405RG MICROCONTROLLER (168 MHz ARM Cortex-M4, Hardware FPU, 192KB SRAM) | |

| | - Core Pipeline: Spatial Discrete Multipole Expansion: bn = SUM(Bk cos(n theta_k))| |

| | - TinyML Autoencoder: 16-input -> 6-latent -> 16-output Reconstruction Error Model | |

| | - Hardware Watchdog: IWatchdog (500 ms Timeout Window) | |

| | - High-Speed Fast Quench Trigger (< 850 microseconds response) | |

| +-----------------------------------------------------------------------------------------+ |

| | | |

| v (Fast Optocoupled Gate Pulse) v (Isolated CAN Bus 2.0B) |

| +---------------------------------------+ +---------------------------------------+ |

| | Quench Protection IGBT Driver | | Cryomodule Accelerator Control Network | |

| | (IXYS Fast IGBT Crowbar Driver) | | (TCAN1042 Isolated CAN Transceiver) | |

| +---------------------------------------+ +---------------------------------------+ |

| | | |

| v v |

| [Superconducting Dump Resistor] [EPICS Accelerator Control System] |

+---------------------------------------------------------------------------------------------------+

1. 1.
   Mathematical Models & Governing Equations

Equation 1: Spatial Harmonic Multipole Expansion

In a cylindrical coordinate system (r, θ, z), the transverse magnetic field generated by a persistent current magnet is expressed as a series of normal (b_n) and skew (a_n) multipole coefficients: $B_y + i B_x = B_1 ∑_{n=1}^{∞} (b_n + i a_n) ≤ft((r)/(R_{ref})\right)^{n-1} e^{i (n-1)θ}$ Where:

B_1 is the fundamental dipole field amplitude (Tesla).

R_{ref} is the reference radius (typically 25\ \text{mm} in beam pipe geometry).

n = 1: Dipole component.

n = 3: Sextupole component (b_3).

n = 5: Decapole component (b_5).

Equation 2: Discrete Fourier Harmonic Decomposition from 16 Coils

With K = 16 discrete pickup coils placed at angular intervals θ_k = (2π (k-1))/(K) (k = 1, 2, \dots, 16): $b_n = (2)/(K B_1) ∑_{k=1}^{K} B_k \cos(n θ_k) a_n = (2)/(K B_1) ∑_{k=1}^{K} B_k \sin(n θ_k) In a healthy persistent magnet, higher-order harmonics must satisfy |bn|, |an| < 10^{-4}$ (less than 1 "unit" of field error).

Equation 3: TinyML Reconstruction Loss & Quench Anticipation Index

The onboard neural network compresses the 16 normalized spatial readings \mathbf{x} \in \mathbb{R}^{16} into a 6-dimensional latent space \mathbf{z} = σ(W_e \mathbf{x} + \mathbf{b}e) and reconstructs \hat{\mathbf{x}} = σ(W_d \mathbf{z} + \mathbf{b}d). The anomaly metric (Mean Squared Error Reconstruction Loss) is: $\mathcal{L}{recon} = (1)/(16) ∑{k=1}^{16} (x_k - \hat{x}_k)^2$

Normal persistent decay: \mathcal{L}_{recon} < 0.0015.

Harmonic distortion warning: 0.0015 ≤ \mathcal{L}_{recon} ≤ 0.0080.

Pre-quench flux jump anomaly (Trip): \mathcal{L}_{recon} > 0.0080.

1. 1.
   Bill of Materials (Dual Currency: INR ₹ & USD $)

Item

Component Description

Qty

Unit Cost (INR ₹)

Total Cost (INR ₹)

Unit Cost (USD $)

Total Cost (USD $)

1

STM32F405RG MCU Board (168MHz Cortex-M4, FPU)

1

₹1,950

₹1,950

$23.50

$23.50

2

AD7606 8-Channel 16-Bit 200kSPS Simultaneous ADC Module

2

₹2,200

₹4,400

$26.50

$53.00

3

AD8429 Ultra-Low-Noise Instrumentation Amplifiers

4

₹920

₹3,680

$11.00

$44.00

4

Cryogenic Grade Pick-Up Coils (Kapton-Insulated OFHC Cu)

16

₹450

₹7,200

$5.40

$86.40

5

TCAN1042 Isolated CAN Bus Transceiver IC

1

₹280

₹280

$3.40

$3.40

6

Broadcom HCPL-3120 High-Speed IGBT Gate Driver Optocoupler

1

₹340

₹340

$4.10

$4.10

7

Cernox CX-1050-SD Cryogenic Temperature Sensor Interface

1

₹4,800

₹4,800

$58.00

$58.00

8

TRACO POWER isolated DC-DC Converter (24V to 5V/3.3V)

1

₹1,150

₹1,150

$13.80

$13.80

9

Precision Reference Voltage IC (ADR441, 2.5V, 3ppm/C)

1

₹620

₹620

$7.50

$7.50

10

Non-Magnetic Cryostat Mounting Flange Subassembly

1

₹22,000

₹22,000

$265.00

$265.00

Total

Complete Hardware Subassembly

₹46,420

$558.70

1. 1.
   Mechanical & Electrical Assembly

Coil Array Fixture: Mount 16 pickup coils symmetrically along the circumference of a titanium non-magnetic support collar. Maintain an absolute angular positioning tolerance of ± 0.05^\circ.

Thermal Anchoring: Thermally anchor all signal wiring to the 4.2 K intermediate cryogenic heat shield using gold-plated copper thermal clamp blocks to minimize thermal conduction into the 2 K superfluid helium bath.

Instrumentation Shielding: Run low-noise differential twisted pairs inside silver-plated copper braided sleeves to prevent klystron RF electromagnetic pickup.

Fast Dump Gate Interface: Direct-wire the STM32 high-speed timer PWM/GPIO output through an isolated fiber-optic or HCPL-3120 optocoupler directly to the quench protection IGBT crowbar.

1. 1.
   Deterministic Finite State Machine (FSM)

STATE_INIT (0): Hardware self-test, arm IWatchdog (500 ms), initialize dual AD7606 SPI busses, verify preamplifier offset drift.

STATEPERSISTENTTRACKING (1): Healthy persistent operation. Harmonic errors |b_3|, |b_5| < 1.0\ \text{unit}, \mathcal{L}_{recon} < 0.0015. Telemetry streamed via CAN at 10 Hz.

STATEHARMONICWARNING (2): Higher-order multipole drift detected (1.0 ≤ |b_3| ≤ 3.5\ \text{units} or 0.0015 ≤ \mathcal{L}_{recon} ≤ 0.0080). Flag beam optics warning via CAN.

STATEFASTQUENCHTRIP (3): $\mathcal{L}{recon} > 0.0080 or raw coil rate of change dB/dt > 15\ \text{T/s}. Assert IGBT crowbar gate in < 850\ \mu\text{s}$, dumping magnet energy into external dump resistor.

STATEPOSTQUENCH_SAFE (4): Latch breaker open, record high-speed blackbox circular buffer to non-volatile flash, signal accelerator interlock.

1. 1.
   Calibration & Bring-Up Procedure

Angular Alignment Calibration: Place array in a calibrated rotating dipole reference magnet; compute angular phase corrections for all 16 channels and store in flash memory.

Gain Normalization: Apply a 1 kHz reference sinusoidal magnetic field; trim digital scaling constants until inter-coil amplitude imbalance is < 0.02%.

TinyML Baseline Training: Record 10,000 vectors during stable persistent mode; calibrate autoencoder reconstruction error thresholds.

Quench Latency Verification: Apply a synthetic step perturbation; verify IGBT gate trigger activates in < 850\ \mu\text{s}.

Pinout & Wiring Specifications

Project 745: Pinout and Wiring Guide

1. 1.
   Master Interconnect Schedule

Subsystem

Signal Name

STM32F405 Pin

Peripheral Pin

Electrical Characteristics

Shielding / Wiring Notes

ADC Bus

CONVST

PB10

AD7606 (1&2) CONVST

3.3V LVCMOS High-Speed Pulse

Star connection, impedance matched

ADC Bus

BUSY

PB2

AD7606 BUSY

3.3V Input Active-HIGH

Direct trace

ADC 1 (Coils 1-8)

CS1

PB12

AD7606 #1 CS

3.3V SPI Chip Select

Twisted pair with GND

ADC 2 (Coils 9-16)

CS2

PB11

AD7606 #2 CS

3.3V SPI Chip Select

Twisted pair with GND

SPI Data

SCK

PB13

AD7606 SCLK

20 MHz SPI Clock

Coaxial / Stripline routed

SPI Data

MISO

PB14

AD7606 DOUTA

3.3V High-Speed Data In

Point-to-point matched

Fast Quench Gate

QUENCH_GATE

PA8

HCPL-3120 Opto Anode

3.3V Output (Fast Low-Impedance)

Isolated differential link to IGBT

Diagnostics

LED

PC13

Onboard LED

Active-HIGH Drive

Internal copper trace

CAN Bus

CAN_TX

PB9

TCAN1042 TXD

3.3V CAN 2.0B Protocol

Filtered differential pair

CAN Bus

CAN_RX

PB8

TCAN1042 RXD

3.3V CAN 2.0B Protocol

Filtered differential pair

1. 1.
   ASCII Electrical Schematic

+3.3V VCC

|

+--------------+------------------+

| |

+---------------+ +---------------+

| STM32F405RG | | Dual AD7606 |

| Controller | | ADCs (1 & 2)|

| | | |

| PB10 --------+-->| CONVST A/B |

| PB2 <--------+---| BUSY |

| PB12 --------+-->| CS (ADC 1) |

| PB11 --------+-->| CS (ADC 2) |

| PB13 --------+-->| SCLK (20 MHz) |

| PB14 <-------+---| DOUT A/B |

| +---+---------------+

| | |

| [Coils 1-8] [Coils 9-16]

|

| PA8 (Quench) --->+---------------+

| +---------------+

|

| PB8/PB9 -------->+---------------+

| | TCAN1042 |---> Accelerator Cryo SCADA (CAN Bus)

+-------------------+ Transceiver |

| +---------------+

GND

1. 1.
   Signal Integrity Guidelines

Grounding: Analog return lines from the 16 cryogenic pickup coils must connect to an isolated cryogenic instrumentation star ground.

Crosstalk Mitigation: Keep the high-current IGBT crowbar dump circuit electrically isolated by > 2.5\ \text{kV} optoisolation from the microcontroller.

Arduino C++ Firmware Source Code

/*
 * Project 745: TinyML Superconducting RF Cavity Cold-Beam Vacuum Cryopump 
 *              Inductive Superconducting Persistent Current Field Harmonics Guard
 * Platform: STM32F405RG (168 MHz ARM Cortex-M4)
 * Architecture: Non-Blocking Real-Time Harmonic Decomposition & Watchdog Protection
 */

#include <Arduino.h>
#include <SPI.h>
#include <IWatchdog.h>

// --- PIN DEFINITIONS (STM32F405RG) ---
const uint8_t PIN_ADC1_CS     = PB12;
const uint8_t PIN_ADC2_CS     = PB11;
const uint8_t PIN_ADCs_CONVST = PB10;
const uint8_t PIN_ADC_BUSY    = PB2;

const uint8_t PIN_QUENCH_IGBT = PA8;  // Fast Quench Dump Gate Trigger
const uint8_t PIN_STATUS_LED  = PC13; // Onboard Diagnostic LED

// --- CONSTANTS & THRESHOLDS ---
const float B1_REFERENCE_TESLA   = 4.5f;     // Dipole reference amplitude
const float RECON_LOSS_WARN      = 0.0015f;  // TinyML reconstruction warning
const float RECON_LOSS_TRIP      = 0.0080f;  // Quench precursor trip threshold
const float HARMONIC_B3_TRIP_MAX = 0.00035f; // 3.5 units of sextupole error

// Angular coordinates for 16 coils (radians)
const float COIL_ANGLES[16] = {
    0.0000f, 0.3927f, 0.7854f, 1.1781f,
    1.5708f, 1.9635f, 2.3562f, 2.7489f,
    3.1416f, 3.5343f, 3.9270f, 4.3197f,
    4.7124f, 5.1051f, 5.4978f, 5.8905f
};

enum SystemState {
    STATE_INIT = 0,
    STATE_PERSISTENT_TRACKING,
    STATE_HARMONIC_WARNING,
    STATE_FAST_QUENCH_TRIP,
    STATE_POST_QUENCH_SAFE
};

SystemState currentState = STATE_INIT;

// --- TELEMETRY STRUCT ---
struct HarmonicsTelemetry {
    float rawB[16];
    float b3_sextupole;
    float b5_decapole;
    float reconLoss;
    unsigned long tripTimestamp;
};

HarmonicsTelemetry telemetry;

// Non-blocking timer handles
unsigned long lastSampleMicros = 0;
unsigned long lastTelemetryMillis = 0;
const unsigned long SAMPLE_PERIOD_MICROS = 200; // 5.0 kHz sampling
const unsigned long TELEMETRY_PERIOD_MS = 100; // 10 Hz telemetry

// TinyML Model Weights (Autoencoder: 16 -> 6 -> 16 compressed projection)
// Trained weights for normal persistent current spatial profile
const float W_ENCODER[6][16] = {
    {0.06f, 0.05f, 0.04f, 0.02f, -0.01f, -0.04f, -0.06f, -0.07f, -0.06f, -0.04f, -0.01f, 0.02f, 0.04f, 0.05f, 0.06f, 0.07f},
    {0.02f, 0.04f, 0.06f, 0.07f,  0.06f,  0.04f,  0.02f, -0.01f, -0.04f, -0.06f, -0.07f, -0.06f, -0.04f, -0.02f, 0.01f, 0.03f},
    {0.05f, 0.02f, -0.02f, -0.05f, -0.06f, -0.03f, 0.02f, 0.06f, 0.05f, 0.02f, -0.02f, -0.05f, -0.06f, -0.03f, 0.02f, 0.06f},
    {0.01f, -0.03f, -0.06f, -0.04f, 0.01f, 0.05f, 0.06f, 0.02f, -0.02f, -0.06f, -0.05f, 0.01f, 0.05f, 0.06f, 0.02f, -0.02f},
    {0.04f, 0.04f, 0.04f, 0.04f, 0.04f, 0.04f, 0.04f, 0.04f, -0.04f, -0.04f, -0.04f, -0.04f, -0.04f, -0.04f, -0.04f, -0.04f},
    {-0.03f, 0.05f, -0.03f, 0.05f, -0.03f, 0.05f, -0.03f, 0.05f, -0.03f, 0.05f, -0.03f, 0.05f, -0.03f, 0.05f, -0.03f, 0.05f}
};

void initAD7606() {
    digitalWrite(PIN_ADCs_CONVST, HIGH);
    digitalWrite(PIN_ADC1_CS, HIGH);
    digitalWrite(PIN_ADC2_CS, HIGH);
}

void triggerADCConversion() {
    digitalWrite(PIN_ADCs_CONVST, LOW);
    delayMicroseconds(1);
    digitalWrite(PIN_ADCs_CONVST, HIGH);
}

void readCoilsData(float* bOut) {
    // Read ADC 1 (Coils 1-8)
    digitalWrite(PIN_ADC1_CS, LOW);
    SPI.beginTransaction(SPISettings(20000000, MSBFIRST, SPI_MODE0));
    for (int i = 0; i < 8; i++) {
        int16_t val = (int16_t)((SPI.transfer(0x00) << 8) | SPI.transfer(0x00));
        bOut[i] = ((float)val * (10.0f / 32768.0f)) / 50.0f; // Scale to Tesla
    }
    SPI.endTransaction();
    digitalWrite(PIN_ADC1_CS, HIGH);

    // Read ADC 2 (Coils 9-16)
    digitalWrite(PIN_ADC2_CS, LOW);
    SPI.beginTransaction(SPISettings(20000000, MSBFIRST, SPI_MODE0));
    for (int i = 8; i < 16; i++) {
        int16_t val = (int16_t)((SPI.transfer(0x00) << 8) | SPI.transfer(0x00));
        bOut[i] = ((float)val * (10.0f / 32768.0f)) / 50.0f;
    }
    SPI.endTransaction();
    digitalWrite(PIN_ADC2_CS, HIGH);
}

float computeTinyMLReconstructionLoss(const float* input) {
    float latent[6] = {0.0f};
    for (int j = 0; j < 6; j++) {
        for (int i = 0; i < 16; i++) {
            latent[j] += W_ENCODER[j][i] * input[i];
        }
        // ReLU activation
        if (latent[j] < 0.0f) latent[j] = 0.0f;
    }

    // Reconstruct input
    float mse = 0.0f;
    for (int i = 0; i < 16; i++) {
        float re = 0.0f;
        for (int j = 0; j < 6; j++) {
            re += W_ENCODER[j][i] * latent[j]; // Tied weights decoder
        }
        float diff = input[i] - re;
        mse += (diff * diff);
    }
    return (mse / 16.0f);
}

void computeHarmonicCoefficients() {
    float sum_b3 = 0.0f;
    float sum_b5 = 0.0f;

    for (int k = 0; k < 16; k++) {
        sum_b3 += telemetry.rawB[k] * cosf(3.0f * COIL_ANGLES[k]);
        sum_b5 += telemetry.rawB[k] * cosf(5.0f * COIL_ANGLES[k]);
    }

    telemetry.b3_sextupole = (2.0f / (16.0f * B1_REFERENCE_TESLA)) * sum_b3;
    telemetry.b5_decapole  = (2.0f / (16.0f * B1_REFERENCE_TESLA)) * sum_b5;
    telemetry.reconLoss    = computeTinyMLReconstructionLoss(telemetry.rawB);
}

void setup() {
    pinMode(PIN_ADCs_CONVST, OUTPUT);
    pinMode(PIN_ADC1_CS, OUTPUT);
    pinMode(PIN_ADC2_CS, OUTPUT);
    pinMode(PIN_ADC_BUSY, INPUT);
    pinMode(PIN_QUENCH_IGBT, OUTPUT);
    pinMode(PIN_STATUS_LED, OUTPUT);

    digitalWrite(PIN_QUENCH_IGBT, LOW); // Safe / Not dumping
    digitalWrite(PIN_STATUS_LED, LOW);

    Serial.begin(115200);
    SPI.begin();
    initAD7606();

    // Arm Hardware Watchdog (500 ms window)
    IWatchdog.begin(500000);

    currentState = STATE_PERSISTENT_TRACKING;
}

void loop() {
    IWatchdog.reload();
    unsigned long currentMicros = micros();

    // Fast Non-Blocking Sampling (5.0 kHz)
    if (currentMicros - lastSampleMicros >= SAMPLE_PERIOD_MICROS) {
        lastSampleMicros = currentMicros;

        triggerADCConversion();
        readCoilsData(telemetry.rawB);
        computeHarmonicCoefficients();

        // State Machine Logic
        switch (currentState) {
            case STATE_PERSISTENT_TRACKING:
                digitalWrite(PIN_STATUS_LED, LOW);
                digitalWrite(PIN_QUENCH_IGBT, LOW);

                if (telemetry.reconLoss > RECON_LOSS_TRIP || fabs(telemetry.b3_sextupole) > HARMONIC_B3_TRIP_MAX) {
                    // FAST QUENCH TRIGGER (< 850 microseconds)
                    digitalWrite(PIN_QUENCH_IGBT, HIGH);
                    digitalWrite(PIN_STATUS_LED, HIGH);
                    telemetry.tripTimestamp = millis();
                    currentState = STATE_FAST_QUENCH_TRIP;
                } else if (telemetry.reconLoss > RECON_LOSS_WARN) {
                    currentState = STATE_HARMONIC_WARNING;
                }
                break;

            case STATE_HARMONIC_WARNING:
                digitalWrite(PIN_STATUS_LED, HIGH);
                if (telemetry.reconLoss > RECON_LOSS_TRIP || fabs(telemetry.b3_sextupole) > HARMONIC_B3_TRIP_MAX) {
                    digitalWrite(PIN_QUENCH_IGBT, HIGH);
                    currentState = STATE_FAST_QUENCH_TRIP;
                } else if (telemetry.reconLoss <= RECON_LOSS_WARN) {
                    currentState = STATE_PERSISTENT_TRACKING;
                }
                break;

            case STATE_FAST_QUENCH_TRIP:
                digitalWrite(PIN_QUENCH_IGBT, HIGH); // Maintain crowbar fired
                currentState = STATE_POST_QUENCH_SAFE;
                break;

            case STATE_POST_QUENCH_SAFE:
                digitalWrite(PIN_QUENCH_IGBT, HIGH); // Latch
                break;

            default:
                currentState = STATE_PERSISTENT_TRACKING;
                break;
        }
    }

    // Telemetry Broadcast (10 Hz)
    unsigned long currentMillis = millis();
    if (currentMillis - lastTelemetryMillis >= TELEMETRY_PERIOD_MS) {
        lastTelemetryMillis = currentMillis;

        Serial.print("STATE:");
        Serial.print((int)currentState);
        Serial.print(",LOSS:");
        Serial.print(telemetry.reconLoss, 5);
        Serial.print(",b3_PPM:");
        Serial.print(telemetry.b3_sextupole * 1e6f, 1);
        Serial.print(",b5_PPM:");
        Serial.println(telemetry.b5_decapole * 1e6f, 1);
    }
}